PRV property and the asymptotic behaviour of solutions of stochastic differential equations
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 funct...
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| Date: | 2005 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2005
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/4424 |
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| Cite this: | 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. |
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Buldygin, V.V. Klesov, O.I. Steinebach, J.G. 2009-11-09T15:30:54Z 2009-11-09T15:30:54Z 2005 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 https://nasplib.isofts.kiev.ua/handle/123456789/4424 519.21 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. This work has partially been supported by Deutsche Forschungsgemeinschaft under DFG grants 436 UKR 113/41/0-3 and 436 UKR 113/68/0-1. en Інститут математики НАН України PRV property and the asymptotic behaviour of solutions of stochastic differential equations Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
PRV property and the asymptotic behaviour of solutions of stochastic differential equations |
| spellingShingle |
PRV property and the asymptotic behaviour of solutions of stochastic differential equations Buldygin, V.V. Klesov, O.I. Steinebach, J.G. |
| title_short |
PRV property and the asymptotic behaviour of solutions of stochastic differential equations |
| title_full |
PRV property and the asymptotic behaviour of solutions of stochastic differential equations |
| title_fullStr |
PRV property and the asymptotic behaviour of solutions of stochastic differential equations |
| title_full_unstemmed |
PRV property and the asymptotic behaviour of solutions of stochastic differential equations |
| title_sort |
prv property and the asymptotic behaviour of solutions of stochastic differential equations |
| author |
Buldygin, V.V. Klesov, O.I. Steinebach, J.G. |
| author_facet |
Buldygin, V.V. Klesov, O.I. Steinebach, J.G. |
| publishDate |
2005 |
| language |
English |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
0321-3900 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/4424 |
| citation_txt |
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. |
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| first_indexed |
2025-12-07T18:31:32Z |
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2025-12-07T18:31:32Z |
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