Reflected backward stochastic evolution equations with jumps in infinite dimensional domains

Hongchao Qian; Hongchao Qian

doi:10.3934/math.2026768

AIMS Mathematics

2026, Volume 11, Issue 6: 18869-18884. doi: 10.3934/math.2026768

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Research article

Reflected backward stochastic evolution equations with jumps in infinite dimensional domains

Hongchao Qian ^,

School of Mathematical Science, Changsha Normal University, Changsha, Hunan 410100, China

Received: 30 March 2026 Revised: 26 May 2026 Accepted: 18 June 2026 Published: 26 June 2026
MSC : 35R60, 60H15

In this paper, we investigated a class of reflected backward stochastic evolution equations with jumps (RBSEEJs). Specifically, the solutions to these equations are constrained to the unit ball of a separable Hilbert space $ H $. We established the existence and uniqueness of such solutions via the penalization method. Finally, an illustrative example demonstrates the applicability of the established theory.
- backward stochastic evolution equation,
- Poisson random mesasure,
- reflection,
- penalization,
- projection
Citation: Hongchao Qian. Reflected backward stochastic evolution equations with jumps in infinite dimensional domains[J]. AIMS Mathematics, 2026, 11(6): 18869-18884. doi: 10.3934/math.2026768

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Abstract

In this paper, we investigated a class of reflected backward stochastic evolution equations with jumps (RBSEEJs). Specifically, the solutions to these equations are constrained to the unit ball of a separable Hilbert space $ H $. We established the existence and uniqueness of such solutions via the penalization method. Finally, an illustrative example demonstrates the applicability of the established theory.

References

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