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The Adapted Solutions for Backward Stochastic Schrödinger Equations with Jumps

Author

Listed:
  • Li Yang

    (School of Mathematical Sciences, Tiangong University, Tianjin 300387, China)

  • Lin Liu

    (School of Mathematical Sciences, Tiangong University, Tianjin 300387, China)

Abstract

This study considers a class of backward stochastic semi-linear Schrödinger equations with Poisson jumps in R d or in its bounded domain of a C 2 boundary, which is associated with a stochastic control problem of nonlinear Schrödinger equations driven by Lévy noise. The approach to establish the existence and uniqueness of solutions is mainly based on the complex Itô formula, the Galerkin’s approximation method, and the martingale representation theorem.

Suggested Citation

  • Li Yang & Lin Liu, 2025. "The Adapted Solutions for Backward Stochastic Schrödinger Equations with Jumps," Mathematics, MDPI, vol. 13(5), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:820-:d:1602918
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    References listed on IDEAS

    as
    1. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    2. Chalishajar, Dimplekumar & Kasinathan, Dhanalakshmi & Kasinathan, Ramkumar & Kasinathan, Ravikumar, 2024. "Exponential stability, T-controllability and optimal controllability of higher-order fractional neutral stochastic differential equation via integral contractor," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    3. Ma, Jin & Yong, Jiongmin, 1997. "Adapted solution of a degenerate backward spde, with applications," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 59-84, October.
    4. Rong, Situ, 1997. "On solutions of backward stochastic differential equations with jumps and applications," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 209-236, March.
    5. Quenez, Marie-Claire & Sulem, Agnès, 2013. "BSDEs with jumps, optimization and applications to dynamic risk measures," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3328-3357.
    6. Roxana Dumitrescu & Bernt Øksendal & Agnès Sulem, 2018. "Stochastic Control for Mean-Field Stochastic Partial Differential Equations with Jumps," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 559-584, March.
    7. Geiss, Christel & Labart, Céline, 2016. "Simulation of BSDEs with jumps by Wiener Chaos expansion," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2123-2162.
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