We study analyticity of the characteristic function of a process defined by means of SDEs. Namely, starting with the simple case of a scalar Ito SDE we show that the corresponding characteristic function is entire. The proof is based on the Gr?enwall’s inequality technique and the classic analyticity criterion in terms of moments. Further, we extend this criterion and derive a handy sufficient condition of analyticity in the multidimensional case. This condition is used to prove the corresponding general result of analyticity. We assume that the drift vector obeys the linear growth condition, and the diffusion matrix is time-onlydependent, but possibly degenerate. The approach used in the article can be extended to more general types of SDEs.
展开▼
机译：我们研究了通过SDE定义的过程的特征函数的分析。即，从Scalar ITO SDE的简单情况下开始，我们显示相应的特征功能是整体的。证明是基于GR？eNWALL的不等式技术和矩的经典分析标准。此外，我们延长了该标准并导出了多维案例中的分析性的方便充分条件。这种情况用于证明分析性的相应一般结果。我们假设漂移量向量遵循线性生长条件，并且扩散矩阵是唯一依赖性，但可能是堕落的。文章中使用的方法可以扩展到更一般的SDE类型。
展开▼
