PRV property and the asymptotic behaviour of solutions of stochastic differential equations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
PRV property and the asymptotic behaviour of solutions of stochastic differential equations
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| Creator |
Buldygin, V.V.
Klesov, O.I. Steinebach, J.G. |
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| Description |
We consider the a.s. asymptotic behaviour of a solution of the stochastic differential equation (SDE) dX(t) = g(X(t))dt + σ(X(t))dW(t), with X(0) ≡ b > 0, where g(.) and σ(.) are positive continuous functions and W(.) is the standard Wiener process. By applying the theory of PRV and PMPV functions, we find the conditions on g(.) and σ(.), under which X(.) resp. f(X(.)) may be approximated a.s. on {X(t)→∞} by μ(.) resp. f(μ(.)), where μ( ) is a solution of the deterministic differential equation dμ(t) = g(μ(t))dt with μ(0) = b, and f(.) is a strictly increasing function. Moreover, we consider the asymptotic behaviour of generalized renewal processes connected with this SDE. |
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| Date |
2009-11-09T15:30:54Z
2009-11-09T15:30:54Z 2005 |
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| Type |
Article
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| Identifier |
PRV property and the asymptotic behaviour of solutions of stochastic differential equations / V.V. Buldygin, O.I. Klesov, J.G. Steinebach // Theory of Stochastic Processes. — 2005. — Т. 11 (27), № 3-4. — С. 42–57. — Бібліогр.: 17 назв.— англ.
0321-3900 http://dspace.nbuv.gov.ua/handle/123456789/4424 519.21 |
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| Language |
en
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| Publisher |
Інститут математики НАН України
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