Backward problems for stochastic differential equations on the Sierpinski gasket

Xuan Liu; Zhongmin Qian

doi:10.1016/j.spa.2017.11.002

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arXiv · 1612.01297

Backward problems for stochastic differential equations on the Sierpinski gasket

Xuan Liu·Zhongmin Qian

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Abstract

In this paper, we study the non-linear backward problems (with deterministic or stochastic durations) of stochastic differential equations on the Sierpinski gasket. We prove the existence and uniqueness of solutions of backward stochastic differential equations driven by Brownian martingale (defined in Section [sec:-1]) on the Sierpinski gasket constructed by S. Goldstein and S. Kusuoka. The exponential integrability of quadratic processes for martingale additive functionals is obtained, and as an application, a Feynman-Kac representation formula for weak solutions of semi-linear parabolic PDEs on the gasket is also established.

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BibTeX RIS

Xuan Liu, Zhongmin Qian. 2016-12-05. Backward problems for stochastic differential equations on the Sierpinski gasket. https://doi.org/10.1016/j.spa.2017.11.002

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