Weak convergence of recursions
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
Year of publication: |
1997
|
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Authors: | Basak, Gopal K. ; Hu, Inchi ; Wei, Ching-Zong |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 68.1997, 1, p. 65-82
|
Publisher: |
Elsevier |
Keywords: | Diffusion Invariant measure Martingale Stochastic differential equation Weak convergence |
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