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Convergence and convergence rates for approximating ergodic means of functions of solutions to stochastic differential equations with Markov switching

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  • Mei, Hongwei
  • Yin, George

Abstract

This work focuses on numerical algorithms for approximating the ergodic means for suitable functions of solutions to stochastic differential equations with Markov regime switching. Our main effort is devoted to obtaining the convergence and rates of convergence of the approximation algorithms. The study is carried out by obtaining laws of large numbers and laws of iterated logarithms for numerical approximation to long-run averages of suitable functions of solutions to switching diffusions.

Suggested Citation

  • Mei, Hongwei & Yin, George, 2015. "Convergence and convergence rates for approximating ergodic means of functions of solutions to stochastic differential equations with Markov switching," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3104-3125.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:8:p:3104-3125
    DOI: 10.1016/j.spa.2015.02.013
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    References listed on IDEAS

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    1. Yuan, Chenggui & Mao, Xuerong, 2003. "Asymptotic stability in distribution of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 277-291, February.
    2. Pettersson, Roger, 1995. "Approximations for stochastic differential equations with reflecting convex boundaries," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 295-308, October.
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    Cited by:

    1. Gilles Pagès & Clément Rey, 2023. "Discretization of the Ergodic Functional Central Limit Theorem," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-44, March.
    2. Pagès Gilles & Rey Clément, 2019. "Recursive computation of the invariant distributions of Feller processes: Revisited examples and new applications," Monte Carlo Methods and Applications, De Gruyter, vol. 25(1), pages 1-36, March.
    3. Gao, Shuaibin & Li, Xiaotong & Liu, Zhuoqi, 2023. "Stationary distribution of the Milstein scheme for stochastic differential delay equations with first-order convergence," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    4. Pagès, Gilles & Rey, Clément, 2020. "Recursive computation of invariant distributions of Feller processes," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 328-365.

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