标题：Stochastic transforms for jump diffusion processes combined with related backward stochastic differential equations(star)
作者：Li, Na;Wu, Zhen
作者机构：[Li, N] School of Mathematics, Shandong University, Jinan, Shandong, 250100, China, Department of Mathematics, QiLu Normal University, Jinan, Shandong 更多
通讯作者地址：[Wu, Z]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
来源：Journal of Mathematical Analysis and Applications
关键词：Backward stochastic differential;equation with jumps;Girsanov theorem;Ito process;Ito-Levy process;Stochastic transform
摘要：This study considers three stochastic transforms for jump diffusion processes: the stochastic Laplace transform, stochastic Fourier transform, and stochastic wavelet transform. First, we introduce the stochastic Laplace transform for processes adapted by Brownian filtration as a solution for complex number valued backward stochastic differential equations (BSDEs). This transform can be explained well by the Girsanov theorem, which also allows us to define the stochastic Laplace transform for jump diffusion processes directly. Based on this Perspective, we give natural definitions of the stochastic Fourier transform and stochastic wavelet transform. The advantages of these stochastic transforms are all related to the uniqueness of the processes. Compared with the classical transforms, the newly introduced parameters guarantee the uniqueness of the stochastic transforms for the adapted processes, while they also agree with the corresponding parameters in the classical transforms, which can represent the frequency property of the processes. In addition,. these three stochastic transforms can also be regarded. as the solutions of related BSDEs with jumps. (C) 2014 Elsevier Inc. All rights reserved.