L^p-Variational solutions of multivalued backward stochastic differential equations

¹ Faculty of Mathematics, “Alexandru Ioan Cuza” University, Carol I Blvd., no. 11, 700506 Iaşi, Romania.
² “Octav Mayer” Institute of Mathematics of the Romanian Academy, Carol I Blvd., no. 8, 700506 Iaşi, Romania.

^* Corresponding author: lucian.maticiuc@uaic.ro

Received: 25 February 2020
Accepted: 6 July 2021

Abstract

We prove the existence and uniqueness of the L^p-variational solution, with p > 1, of the following multivalued backward stochastic differential equation with p-integrable data: {−dY_t + ∂_yΨ(t,Y_t)dQ_t∋H(t,Y_t,Z_t)dQ_t−Z_tdB_t,0≤t<τ, Y_τ = η,

where τ is a stopping time, Q is a progressively measurable increasing continuous stochastic process and ∂_yΨ is the subdifferential of the convex lower semicontinuous function y↦Ψ(t, y). In the framework of [14] (the case p ≥ 2), the strong solution found it there is the unique variational solution, via the uniqueness property proved in the present article.