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Weak convergence of recursions

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  • Basak, Gopal K.
  • Hu, Inchi
  • Wei, Ching-Zong

Abstract

In this paper, we study the asymptotic distribution of a recursively defined stochastic process where are d-dimensional random vectors, b, d --> d and [sigma]: d --> d x r are locally Lipshitz continuous functions, {[var epsilon]n} are r-dimensional martingale differences, and {an} is a sequence of constants tending to zero. Under some mild conditions, it is shown that, even when [sigma] may take also singular values, {Xn} converges in distribution to the invariant measure of the stochastic differential equation where is a r-dimensional Brownian motion

Suggested Citation

  • Basak, Gopal K. & Hu, Inchi & Wei, Ching-Zong, 1997. "Weak convergence of recursions," Stochastic Processes and their Applications, Elsevier, vol. 68(1), pages 65-82, May.
    • Handle: RePEc:eee:spapps:v:68:y:1997:i:1:p:65-82
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    References listed on IDEAS

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    1. Basak, Gopal K., 1991. "A class of limit theorems for singular diffusions," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 44-59, October.
    2. Bhattacharya, R. N. & Ramasubramanian, S., 1982. "Recurrence and ergodicity of diffusions," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 95-122, March.
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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. Gopal K. Basak & Amites Dasgupta, 2006. "Central and Functional Central Limit Theorems for a Class of Urn Models," Journal of Theoretical Probability, Springer, vol. 19(3), pages 741-756, December.
    3. Honoré, Igor, 2020. "Sharp non-asymptotic concentration inequalities for the approximation of the invariant distribution of a diffusion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2127-2158.
    4. 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.
    5. Amarjit Budhiraja & Jiang Chen & Sylvain Rubenthaler, 2014. "A Numerical Scheme for Invariant Distributions of Constrained Diffusions," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 262-289, May.
    6. 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.
    7. Panloup, Fabien, 2009. "A connection between extreme value theory and long time approximation of SDEs," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3583-3607, October.

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