AbstractWe study a class of integrable and discontinuous measure‐valued branching processes. They are constructed as limits of renormalized spatial branching processes, the underlying branching distribution belonging to the domain of attraction of a stable law. These processes, computed on a test functionf, are semimartingales whose martingale terms are identified with integrals offwith respect to a martingale measure. According to a representation theorem of continuous (respectively purely discontinuous) martingale measures as stochastic integrals with respect to a white noise (resp. to a POISSON process), we prove that the measure‐valued processes that we consider are solutions of stochastic differential equations in the space ofL2(Ω)‐valued vector me
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机译:摘要我们研究了一类可积和不连续的测值分支过程。它们被构造为重整化空间分支过程的极限,即属于稳定定律吸引力域的潜在分支分布。这些过程在测试函数f上计算,是半鞅,其鞅项与鞅测度的积分相符。根据连续(分别是纯不连续的)鞅测度作为关于白噪声的随机积分的表示定理(类似于泊松过程),我们证明了我们考虑的测值过程是 L2(Ω) 值向量 me 空间中的随机微分方程的解
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