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Ergodic behavior of diffusions with random jumps from the boundary

Author

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  • Ben-Ari, Iddo
  • Pinsky, Ross G.

Abstract

We consider a diffusion process on , which upon hitting [not partial differential]D, is redistributed in D according to a probability measure depending continuously on its exit point. We prove that the distribution of the process converges exponentially fast to its unique invariant distribution and characterize the exponent as the spectral gap for a differential operator that serves as the generator of the process on a suitable function space.

Suggested Citation

  • Ben-Ari, Iddo & Pinsky, Ross G., 2009. "Ergodic behavior of diffusions with random jumps from the boundary," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 864-881, March.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:3:p:864-881
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    Cited by:

    1. Peng, Jun, 2014. "A note on the first passage time of diffusions with holding and jumping boundary," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 58-64.
    2. Pinsky, Ross G., 2020. "Diffusive search with spatially dependent resetting," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2954-2973.
    3. Kumar Muthuraman & Sridhar Seshadri & Qi Wu, 2015. "Inventory Management with Stochastic Lead Times," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 302-327, February.
    4. Jiatu Cai & Mathieu Rosenbaum & Peter Tankov, 2015. "Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach," Papers 1510.04295, arXiv.org.

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