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

Hani Abidi; Rim Amami; Roger Pettersson; Chiraz Trabelsi

doi:10.1108/AJMS-09-2023-0024

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

Hani Abidi
, Rim Amami^*
, Roger Pettersson
, Chiraz Trabelsi

^*Corresponding author for this work

Department of Basic Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	82-95
Number of pages	14
Journal	Arab Journal of Mathematical Sciences
Volume	31
Issue number	1
DOIs	https://doi.org/10.1108/AJMS-09-2023-0024
State	Published - 27 Jan 2025

Keywords

Backward stochastic differential equation with jumps
Gelfand triple
Yosida approximation

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10.1108/AJMS-09-2023-0024

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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.",

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author = "Hani Abidi and Rim Amami and Roger Pettersson and Chiraz Trabelsi",

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T1 - L2-convergence of Yosida approximation for semi-linear backward stochastic differential equation with jumps in infinite dimension

AU - Abidi, Hani

AU - Amami, Rim

AU - Pettersson, Roger

AU - Trabelsi, Chiraz

PY - 2025/1/27

Y1 - 2025/1/27

N2 - 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.

AB - 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.

KW - Backward stochastic differential equation with jumps

KW - Gelfand triple

KW - Yosida approximation

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DO - 10.1108/AJMS-09-2023-0024

M3 - Article

AN - SCOPUS:85182424087

SN - 1319-5166

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SP - 82

EP - 95

JO - Arab Journal of Mathematical Sciences

JF - Arab Journal of Mathematical Sciences

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ER -

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

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Keywords

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