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Ergodic BSDEs and related PDEs with Neumann boundary conditions

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  • Richou, Adrien

Abstract

We study a new class of ergodic backward stochastic differential equations (EBSDEs for short) which is linked with semi-linear Neumann type boundary value problems related to ergodic phenomena. The particularity of these problems is that the ergodic constant appears in Neumann boundary conditions. We study the existence and uniqueness of solutions to EBSDEs and the link with partial differential equations. Then we apply these results to optimal ergodic control problems.

Suggested Citation

  • Richou, Adrien, 2009. "Ergodic BSDEs and related PDEs with Neumann boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2945-2969, September.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:9:p:2945-2969
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    Cited by:

    1. Li, Juan & Zhao, Nana, 2019. "Representation of asymptotic values for nonexpansive stochastic control systems," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 634-673.
    2. Robertson, Scott & Xing, Hao, 2015. "Large time behavior of solutions to semi-linear equations with quadratic growth in the gradient," LSE Research Online Documents on Economics 60578, London School of Economics and Political Science, LSE Library.
    3. Gechun Liang & Thaleia Zariphopoulou, 2015. "Representation of homothetic forward performance processes in stochastic factor models via ergodic and infinite horizon BSDE," Papers 1511.04863, arXiv.org, revised Nov 2016.
    4. Madec, P.Y., 2015. "Ergodic BSDEs and related PDEs with Neumann boundary conditions under weak dissipative assumptions," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1821-1860.
    5. Maticiuc, Lucian & Răşcanu, Aurel, 2016. "On the continuity of the probabilistic representation of a semilinear Neumann–Dirichlet problem," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 572-607.
    6. Debussche, Arnaud & Hu, Ying & Tessitore, Gianmario, 2011. "Ergodic BSDEs under weak dissipative assumptions," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 407-426, March.

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