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Teoriya Veroyatnostei i ee Primeneniya, 1979, Volume 24, Issue 4, Pages 866–872
(Mi tvp2914)
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Short Communications
On the strong convergence of the sequence of diffusion type processes
S. I. Pisanec Institute of Cybernetics AS Ukrainian SSR, Kiev
Abstract:
Let $\xi_t^{(n)}$, $t\le T$ be the sequence of solutions of stochastic differential equations
$$
d\xi_t^{(n)}=\alpha_t^{(n)}(\xi_t^{(n)})\,dt+dw_t,\qquad\xi_t^{(n)}=0,\qquad n=0,1,\dots
$$
In this paper we study the conditions under which
$$
\lim_{n\to\infty}\mathbf M\biggl|\int_0^t\alpha_s^{(n)}(w)\,ds-
\int_0^t\alpha_s^{(0)}(w)\,ds\biggr|^2=0,\qquad t\le T,
$$
and the conditions under which
$$
\lim_{n\to\infty}\mathbf M|\xi_t^{(n)}-\xi_t^{(0)}|^2=0,\qquad t\le T.
$$
Received: 10.10.1977
Citation:
S. I. Pisanec, “On the strong convergence of the sequence of diffusion type processes”, Teor. Veroyatnost. i Primenen., 24:4 (1979), 866–872; Theory Probab. Appl., 24:4 (1980), 863–869
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https://www.mathnet.ru/eng/tvp2914 https://www.mathnet.ru/eng/tvp/v24/i4/p866
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Abstract page: | 148 | Full-text PDF : | 76 |
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