A Class of Backward Doubly Stochastic Differential Equations with Discontinuous Coefficients
Qingfeng Zhu, Yufeng Shi
TL;DR
This paper investigates the existence of solutions for a class of backward doubly stochastic differential equations with discontinuous coefficients, establishing conditions under which solutions exist and providing a comparison theorem.
Contribution
It introduces new existence results for BDSDEs with left-Lipschitz, possibly discontinuous coefficients, and derives a comparison theorem for these equations.
Findings
Existence of solutions for BDSDEs with discontinuous coefficients.
A comparison theorem for these BDSDEs.
Conditions under which solutions are guaranteed.
Abstract
In this work the existence of solutions of one-dimensional backward dou- bly stochastic differential equations (BDSDEs in short) where the coefficient is left-Lipschitz in y (may be discontinuous) and Lipschitz in z is studied. Also, the associated comparison theorem is obtained.
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Taxonomy
TopicsStochastic processes and financial applications · Differential Equations and Numerical Methods · Nonlinear Differential Equations Analysis