L2-convergence of Yosida approximation for semi-linear backward stochastic differential equation with jumps in infinite dimension

Abstract

Purpose – The main motivation of this paper is to present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L2-convergence rate is established. Design/methodology/approach – The authors establish a result concerning the L2-convergence rate of the solution of backward stochastic differential equation with jumps with respect to the Yosida approximation. Findings – The authors carry out a convergence rate of Yosida approximation to the semi-linear backward stochastic differential equation in infinite dimension. Originality/value – In this paper, the authors present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L2-convergence rate is established.

Keywords

• Backward stochastic differential equation with jumps
• Gelfand triple
• Yosida approximation