Weak convergence of recursions

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

Stochastic Processes and their Applications, 1997, vol. 68, issue 1, 65-82

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

Keywords: Diffusion; Invariant; measure; Martingale; Stochastic; differential; equation; Weak; convergence (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (7)

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