Backward Stochastic Evolution Inclusions in UMD Banach Spaces

2022/04/28 by El Hassan Essaky, Essaky, E. H., M. Hassani +3
Economics, Econometrics and Finance · Mathematics · Computer Science · #Stochastic processes and financial applications #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2204.13389

Abstract

In this paper, we prove the existence of a mild L^p-solution for the backward stochastic evolution inclusion (BSEI for short) of the form % \begincases dY_t+AY_tdt∈ G(t,Y_t,Z_t)dt+Z_tdW_t, t∈ [0,T] Y_T =ξ, \endcases where W=(W_t)_{t∈ [0,T]} is a standard Brownian motion, A is the generator of a C₀-semigroup on a UMD Banach space E, ξ is a terminal condition from L^p(Ω,\mathscrF_T;E), with p>1 and G is a set-valued function satisfying some suitable conditions. The case when the processes with values in spaces that have martingale type 2, has been also studied.

Related

• Backward stochastic evolution equations in UMD Banach spaces
• Stochastic evolution equations in UMD Banach spaces
• Infinitely delayed stochastic evolution equations in UMD Banach spaces
• Weak solutions of backward stochastic differential equations with continuous generator
• \mathbbL^p (p>1)-solutions for BSDEs with jumps and stochastic monotone generator