Stochastic differential games with competing Brownian particles and related Isaacs' equations

Feng Xinwei

摘要

Summary >In this paper, we study zero‐sum two‐player stochastic differential games in which the state equations are competing Brownian particles and the cost functional is defined by generalized backward stochastic differential equations with more than one increasing process. After we study the regularity of competing Brownian particles, we establish the dynamic programming principle for the upper and lower value functions and show that these are the unique viscosity solution of the associated upper and lower Isaacs' equations, which are fully nonlinear parabolic partial differential equations with nonlinear Neumann boundary conditions. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract XMLNS =“http://www.wiley.com/namespaces/wiley”type =“main”xml：lang =“en”xml：id =“oca2356-abs-abs-0001”> <标题类型=“main” >摘要</ title> >在本文中，我们研究零和两者随机差动差动游戏，其中状态方程是竞争褐色粒子，并且通过具有多于一个增加的广义的向后随机微分方程来定义成本函数过程。在我们研究竞争褐色粒子的规律之后，我们建立了上下价值和下部值的动态规划原理，并表明这些是相关的上下索兰和下部的独特粘度解，这是完全非线性抛物面的偏微分方程具有非线性Neumann边界条件。</ p> </ abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-27675/'>《Optimal Control Applications and Methods》</a> <b style="margin: 0 2px;">|</b><span>2018年第2期</span><b style="margin: 0 2px;">|</b><span>共18页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Feng Xinwei&option=202" target="_blank" rel="nofollow">Feng Xinwei;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>School of MathematicsShandong UniversityJinan 250100 China;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/1147.html" title="应用数学">应用数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=competing Brownian particles&option=203" rel="nofollow">competing Brownian particles;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=dynamic programming principle&option=203" rel="nofollow">dynamic programming principle;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=generalized backward stochastic differential equations&option=203" rel="nofollow">generalized backward stochastic differential equations;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=partial differential equations&option=203" rel="nofollow">partial differential equations;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=stochastic differential games&option=203" rel="nofollow">stochastic differential games;</a> </p> <div class="translation"> 机译：竞争棕色粒子;动态编程原理;广义落后随机微分方程;部分微分方程;随机差动游戏; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704024161056.html">Stochastic differential games with competing Brownian particles and related Isaacs' equations</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Feng Xinwei&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Feng Xinwei </a> <a href="/journal-foreign-27675/" target="_blank" rel="nofollow" class="tuijian_authcolor">Optimal Control Applications and Methods .</a> <span>2018</span><span>,第2期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：与竞争褐色粒子和相关ISAACS方程的随机差动游戏</span> </p> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/070409003096.html">Stochastic differential games and viscosity solutions of Hamilton-Jacobi-Bellman-Isaacs equations</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Buckdahn R&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Buckdahn R,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Li J&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Li J </a> <a href="/journal-foreign-28151/" target="_blank" rel="nofollow" class="tuijian_authcolor">SIAM Journal on Control and Optimization .</a> <span>2008</span><span>,第1期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：Hamilton-Jacobi-Bellman-Isaacs方程的随机微分对策和粘性解</span> </p> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/academic-journal-foreign_detail_thesis/0204116153493.html">Stochastic differential games and viscosity solutions of Isaacs equations</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Makiko Nisio&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Makiko Nisio </a> <a href="/journal-foreign-25517/" target="_blank" rel="nofollow" class="tuijian_authcolor">Nagoya Mathematical Journal .</a> <span>1988</span><span>,第3期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：Isaacs方程的随机微分对策和粘度解</span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/academic-conference-foreign_meeting-202979_thesis/020513932101.html">Path-dependent differential games of inf-sup type and Isaacs partial differential equations</a> <b>[C]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Hidehiro Kaise&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Hidehiro Kaise </a> <a href="/conference-foreign-202979/" target="_blank" rel="nofollow" class="tuijian_authcolor">IEEE Conference on Decision and Control .</a> <span>2015</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：inf-sup型路径相关的微分对策和Isaacs偏微分方程</span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/academic-degree-foreign_mphd_thesis/02061317663.html">Malliavin calculus for backward stochastic differential equations and stochastic differential equations driven by fractional Brownian motion and numerical schemes.</a> <b>[D] </b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Song, Xiaoming.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Song, Xiaoming. </a> <span>2011</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：Malliavin演算，用于分数布朗运动和数值格式驱动的后向随机微分方程和随机微分方程。</span> </p> </li> <li> <div> <b>6. </b><a class="enjiyixqcontent" href="/academic-journal-foreign-pmc_springer-open-choice_thesis/040004925685.html">Exponential stability for neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion</a> <b>[O] </b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Xinwen Zhang&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Xinwen Zhang,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Dehao Ruan&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Dehao Ruan </a> <span>-1</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：由布朗运动和分数布朗运动驱动的中立型随机泛函偏微分方程的指数稳定性。</span> </p> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/open-access_resources_thesis/0100090170117.html ">Integral-Partial Differential Equations of Isaacs' Type Related to Stochastic Differential Games with Jumps</a> <b>[O] </b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Buckdahn, Rainer&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Buckdahn, Rainer,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Hu, Ying&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Hu, Ying,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Li, Juan&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Li, Juan </a> <span>2010</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：Isaacs型的积分 - 偏微分方程具有跳跃的随机微分对策</span> </p> </li> <li> <div> <b>8. </b><a class="enjiyixqcontent" href="/ntis-science-report_ad_thesis/020711494954.html">Differential Games, Optimal Control and Directional Derivatives of Viscosity Solutions of Bellman's and Isaacs' Equations</a> <b>[R] </b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Lions, P. L.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Lions, P. L.,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Souganidis, P. E.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Souganidis, P. E. </a> <span>1985</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：Bellman和Isaacs方程粘性解的微分对策，最优控制和方向导数</span> </p> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/academic-journal-cn_transactions-chinese-society-agricultural-engineering_thesis/0201258206896.html">基于随机粒子群算法的Van Genuchten方程参数优化求解</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=陈大春&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 陈大春</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=马英杰&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,马英杰</a> <span> <a href="/journal-cn-6826/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 农业工程学报 </a> </span> <span> . 2006</span><span>,第012期</span> </span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/academic-journal-cn_journal-xiangtan-normal-university-natural-science-edition_thesis/0201248782688.html">Ito-Skorohod随机微分方程——非Lipschitz条件下方程的解与解的相关性质</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=尹湘锋&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 尹湘锋</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=张志武&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,张志武</a> <span> <a href="/journal-cn-4575/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 湘潭师范学院学报（自然科学版） </a> </span> <span> . 2009</span><span>,第001期</span> </span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/academic-journal-cn_acta-physica-sinica_thesis/0201250876039.html">纳米静态随机存储器质子单粒子多位翻转角度相关性研究∗</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=罗尹虹&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 罗尹虹</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=张凤祁&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,张凤祁</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=郭红霞&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,郭红霞</a> <span> <a href="/journal-cn-15096/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 物理学报 </a> </span> <span> . 2015</span><span>,第021期</span> </span> </div> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/academic-journal-cn_detail_thesis/0201296305368.html">非常密集随机分布球粒子相关散射的数值模拟</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=杨青&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 杨青</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=金亚秋&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,金亚秋</a> <span> <a href="/journal-cn-57258/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 计算物理 </a> </span> <span> . 2006</span><span>,第4期</span> </span> </div> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/academic-journal-cn_international-journal-pathology-clinical-medicine_thesis/0201281733765.html">CASPR2抗体相关的Isaacs综合征1例</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=张凌峰&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 张凌峰</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=刘彬&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,刘彬</a> <span> <a href="/journal-cn-5753/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 国际病理科学与临床杂志 </a> </span> <span> . 2020</span><span>,第012期</span> </span> </div> </li> <li> <div> <b>6. </b><a class="enjiyixqcontent" href="/academic-conference-cn_meeting-18415_thesis/020222016352.html">与年龄相关的带跳随机种群方程半隐式Euler方法的收敛性</a> <b>[C]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=王拉省&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 王拉省</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=孙洁&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,孙洁</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=黄斌&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,黄斌</a> <span> <a href="/conference-cn-18415/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 2008年国际应用统计学术研讨会 </a> <span> <span> . 2008</span> </span> </div> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/academic-degree-domestic_mphd_thesis/020313618732.html">带随机违约时间的倒向随机微分方程，超前倒向随机微分方程及其相关结果</a> <b>[A] </b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=许晓明&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 许晓明</a> <span> . 2010</span> </span> </div> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/patent-detail/06120111429492.html">一种游戏中通过随机数点竞争特殊场景的方法</a> <b>[P]</b> . <span> 中国专利： CN108939541A </span> <span> . 2018-12-07</span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/patent-detail/061201043834.html">处理一竞争式随机存取程序的方法及其相关通讯装置</a> <b>[P]</b> . <span> 中国专利： CN101534565B </span> <span> . 2012.10.31</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130403645412.html">STOCHASTIC DIFFERENTIAL EQUATIONS SOLVER</a> <b>[P]</b> . <span> 外国专利：  WO2018235004A1 </span> <span> . 2018-12-27</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：随机微分方程求解器 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130495731360.html">Means for integrating of systems ordinary differential equations of any desired order, for example by differential equations for oscillation before</a> <b>[P]</b> . <span> 外国专利：  DE510840C </span> <span> . 1930-11-22</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：用于积分系统任何所需阶数的常微分方程的装置，例如通过振荡前的微分方程 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130495757388.html">establishment of systems to integrate differential equations of arbitrary order usual bone, e.g. differential equations for schwingungsvorgaenge</a> <b>[P]</b> . <span> 外国专利：  DE000000510840A </span> <span> . 1930-11-22</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：建立集成任意阶数通常骨骼的微分方程的系统，例如schwingungsvorgaenge的微分方程 </span> </p> </li> </ul> </div> </div> </div> <div class="theme cardcommon" style="overflow: auto;display:none"> <h3 class="all_title" id="enpatent55">相关主题</h3> <ul id="subject"> </ul> </div> </div> </div> </div> <div class="right rightcon"> <div class="details_img cardcommon clearfix" style="margin-bottom: 10px;display:none;" > </div> </div> </div> <div id="thesis_get_original1" class="downloadBth" style="bottom: 19px;z-index: 999;" onclick="ywcd('0704024161056','4',7,2,1,'',this,24)" class="delivery" prompt="010401" title="通过人工服务将文献原文发送至邮箱" >获取原文</div> <div class="journalsub-pop-up" style="display: none"> <div class="journal-sub"> <h2>期刊订阅</h2> <img src="https://cdn.zhangqiaokeyan.com/img/loginclose.png" alt="关闭" onclick="$('.journalsub-pop-up').hide()"> <p class="pardon">抱歉，该期刊暂不可订阅，敬请期待！</p> <p class="current">目前支持订阅全部北京大学中文核心（2020）期刊目录。</p> <div style="display: flex;margin-top: 69px;justify-content: space-between;"> <div class="no-sub" onclick="$('.journalsub-pop-up').hide()">暂不订阅</div> <div class="other-sub" onclick="continueSub('from=pc-detail')">继续订阅其他期刊</div> </div> </div> </div> <div class="right_btn"> <ul> <li class="gouwuche">  </li> <li class="yijian"> <a href="javascript:void(0);" onclick="link_analysis('/mycenter/auth/complaint.html',this)" title="意见反馈">意见反馈</a> </li> <li class="top"> <a href="javascript:scrollTo(0,0);" title="回到顶部">回到顶部</a> </li> <li class="shouye"> <a href="/" title="首页">回到首页</a> </li> </ul> </div> <div class="xllindexfooter"> <div class="xllindexfootercenter"> <div class="xllindexfooterleft left" > <div class="xllindexfooterleftli"> <ul> <li><a href="/about.html" title="关于掌桥">关于掌桥</a></li> <li><a href="/help/helpmap.html" title="资源导航">资源导航</a></li> <li><a href="/help/helpguide.html" title="新手指南">新手指南</a></li> <li><a href="/help/helpcenter.html" title="常见问题">常见问题</a></li> <li><a href="/sitemap.html" title="网站地图">网站地图</a></li> <li><a href="/help/helpcenter.html?type=9" title="版权声明">版权声明</a></li> </ul> </div> <div class="xllindexfooterleft"> <p class="xllindexfooterlefteamil">客服邮箱：kefu@zhangqiaokeyan.com</p> <div class="xllindexfooterlefttcp"> <div class="xllindexfooterpoliceiimg"></div> <div class="xllindexfooterpoliceispan"> <span>京公网安备：11010802029741号 </span> <span>ICP备案号：<a href="https://beian.miit.gov.cn" rel="nofollow" target="_blank" title="ICP备案号">京ICP备15016152号-6</a></span> <span>六维联合信息科技 (北京) 有限公司©版权所有</span> </div> </div> </div> </div> <div class="xllindexfooterright left"> <ul> <li> <p style="font-weight: bold;">客服微信</p> <div></div> </li> <li> <p style="font-weight: bold;">服务号</p> <div></div> </li> </ul> </div> </div> </div> <span id="0704024161056down" data-source="7," data-out-id="TtrBJtNGxH/gubr7qoIrjQ==," data-f-source-id="7" data-title="Stochastic differential games with competing Brownian particles and related Isaacs' equations" data-price="20" data-site-name="" data-transnum="24" style="display:none;"></span> <input type="hidden" value="4" id="sourcetype"> <input type="hidden" value="27675" id="journalid"> <input type="hidden" value="1" id="inyn_provide_service_level"> <input type="hidden" value="https://cdn.zhangqiaokeyan.com" id="imgcdn"> <input type="hidden" value="1" id="isdeatail"> <input type="hidden" value="" id="syyn_indexed_database"> <input type="hidden" value="" id="servicetype"> <input type="hidden" id="pagename" value="Stochastic differential games with competing Brownian particles and related Isaacs' equations"/> <input type="hidden" value="thesis_get_original" id="pageIdentification"> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/jquery-1.12.4.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/lwlh_ajax.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/zq.js?v=5.7.8"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/common.js?v=5.7.8"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/jquery.cookie.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/top.js?v=5.7.8"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/tip.js?v=5.7.8"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/login.js?v=5.7.8"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/down.js?v=5.7.8"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/search.js?v=5.7.8"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/newmail.js?v=5.7.8"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/searchtype.js?v=5.7.8"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/user/regist.js?v=5.7.8"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/zxs_solor/detail.js?v=5.7.8"></script> <script type="text/javascript" src="https://www.zhangqiaokeyan.com/statistics/static/pagecollection.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/tj.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/sse.js?v=5.7.8"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/pushbaidu.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/history.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/util/cookie.js?v=5.7.8"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/weipu/weipu.js?v=5.7.8"></script> </body> <script> $(function(){ var weiPuStatus = getCookie('WeiPuStatus'); if(weiPuStatus){ tipWeiPuStatus(weiPuStatus); delCookie('WeiPuStatus'); } getFacetKeywordVoInId(); var sourcetype = $("#sourcetype").val(); var inyn_provide_service_level = $("#inyn_provide_service_level").val(); if((sourcetype ==1||sourcetype==4)&&inyn_provide_service_level!=4){ getJournal(); } }) </script> </html>