Explicit Solution of Infinite-Horizon Linear Backward Stochastic Volterra Integral Equations
Probability
2026-03-17 v1
Abstract
We study linear backward stochastic Volterra integral equations (BSVIEs) on the infinite time horizon. By introducing weighted function spaces with exponential decay, we establish existence and uniqueness of adapted M-solutions. We construct an infinite-horizon resolvent kernel and derive explicit formulas for the solution components (Y,Z,K) using a Girsanov transformation and Hida-Malliavin calculus. The results extend the finite-horizon theory of Hu and Oksendal to the infinite horizon framework.
Keywords
Cite
@article{arxiv.2603.15479,
title = {Explicit Solution of Infinite-Horizon Linear Backward Stochastic Volterra Integral Equations},
author = {Samia Yakhlef and Hilel Ardjan},
journal= {arXiv preprint arXiv:2603.15479},
year = {2026}
}