报告题目：Stochastic Transforms for Jump Diffusion Processes Combined with Related Backward Stochastic Differential Equations
时 间：2017年5月18日（星期四）上午10:30-12:00
报 告 人：李娜副教授
地 点：18-918（理学院会议室）
摘 要：This talk is to introduce 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.
专家简介：李娜，山东财经大学副教授，山东大学博士，师从“国家杰出青年科学基金”获得者、长江学者吴臻教授，主要研究方向为金融数学、随机分析与随机控制，发表论文12篇，其中5篇被SCI收录，2篇被EI收录，现主持山东省高等学校科技计划项目一项，数次参加国内外会议并做会议报告。
