Infinite-Horizon Stochastic Recursive Differential Games with Jumps: Nonautonomous Coefficients and Nonzero Terminal Values
Abstract
In this paper, we investigate a class of decoupled infinite-horizon forward--backward stochastic differential equations (FBSDEs) with time-dependent coefficients and jumps. Under suitable time-integrability conditions on the coefficient growth and stochastic Lipschitz moduli, we establish an Lp theory (p≥ 2) for these systems, including well-posedness, moment estimates, conditional stability, and tail estimates, without imposing dissipativity of the forward dynamics or monotonicity of the backward generator in its value variable. In particular, the forward state converges in Lp and almost surely to a limiting random variable X∞, while the backward solution converges to the generally nonzero terminal value Φ(X∞). Within this framework, we study infinite-horizon two-player zero-sum stochastic recursive differential games. We prove that the lower and upper value functions are deterministic and establish the dynamic programming principle (DPP) using backward stochastic semigroups and nonanticipative strategies. Both value functions converge locally uniformly to Φ as the initial time tends to infinity and are characterized as viscosity solutions of the corresponding non-autonomous, nonlocal Hamilton--Jacobi--Bellman--Isaacs (HJBI) equations. Under an additional integrable Lyapunov-barrier condition, we establish a comparison principle for continuous viscosity subsolutions and supersolutions of uniform linear growth, provided that at least one is uniformly Lipschitz in space. This yields uniqueness for both HJBI equations in the linear-growth class. Finally, we establish a weaker, contact-wise Isaacs criterion ensuring that the lower and upper value functions coincide and hence that the game has a value.
Related
- Multidimensional Infinite-Horizon Markovian Backward Stochastic Differential Equations with Continuous Coefficients and Nonzero-Sum Differential Games
- Recursive Stochastic Linear-Quadratic Control with Indefinite Weights for Jump-Diffusion Systems with Random Coefficients
- Pathwise uniqueness for degenerate stochastic differential equations with Hölder continuous coefficients
- Backward stochastic partial differential equations with unbounded random coefficients
- Stochastic differential games with random coefficients and state constraints: associated stochastic Hamilton-Jacobi-Bellman-Isaacs equations with Neumann boundary conditions
BibTeX
@misc{luo2026infinitehorizon,
title = {{Infinite-Horizon Stochastic Recursive Differential Games with Jumps: Nonautonomous Coefficients and Nonzero Terminal Values}},
author = {Sheng Luo and Qingmeng Wei and Yaxin Wen},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04143},
eprint = {2611.04143},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04143},
}
RIS
TY - UNPB
TI - Infinite-Horizon Stochastic Recursive Differential Games with Jumps: Nonautonomous Coefficients and Nonzero Terminal Values
AU - Sheng Luo
AU - Qingmeng Wei
AU - Yaxin Wen
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04143
UR - https://arxiv.org/abs/2611.04143
AB - In this paper, we investigate a class of decoupled infinite-horizon forward--backward stochastic differential equations (FBSDEs) with time-dependent coefficients and jumps. Under suitable time-integrability conditions on the coefficient growth and stochastic Lipschitz moduli, we establish an L^p theory (p≥ 2) for these systems, including well-posedness, moment estimates, conditional stability, and tail estimates, without imposing dissipativity of the forward dynamics or monotonicity of the backward generator in its value variable. In particular, the forward state converges in L^p and almost surely to a limiting random variable X_∞, while the backward solution converges to the generally nonzero terminal value Φ(X_∞). Within this framework, we study infinite-horizon two-player zero-sum stochastic recursive differential games. We prove that the lower and upper value functions are deterministic and establish the dynamic programming principle (DPP) using backward stochastic semigroups and nonanticipative strategies. Both value functions converge locally uniformly to Φ as the initial time tends to infinity and are characterized as viscosity solutions of the corresponding non-autonomous, nonlocal Hamilton--Jacobi--Bellman--Isaacs (HJBI) equations. Under an additional integrable Lyapunov-barrier condition, we establish a comparison principle for continuous viscosity subsolutions and supersolutions of uniform linear growth, provided that at least one is uniformly Lipschitz in space. This yields uniqueness for both HJBI equations in the linear-growth class. Finally, we establish a weaker, contact-wise Isaacs criterion ensuring that the lower and upper value functions coincide and hence that the game has a value.
ER -