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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| Дата: | 2005 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2005
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| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/4424 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-44242009-11-10T12:00:30Z PRV property and the asymptotic behaviour of solutions of stochastic differential equations Buldygin, V.V. Klesov, O.I. Steinebach, J.G. 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. 2005 Article 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 en Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Buldygin, V.V. Klesov, O.I. Steinebach, J.G. |
| spellingShingle |
Buldygin, V.V. Klesov, O.I. Steinebach, J.G. PRV property and the asymptotic behaviour of solutions of stochastic differential equations |
| author_facet |
Buldygin, V.V. Klesov, O.I. Steinebach, J.G. |
| author_sort |
Buldygin, V.V. |
| title |
PRV property and the asymptotic behaviour of solutions of stochastic differential equations |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2005 |
| url |
http://dspace.nbuv.gov.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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2023-03-24T08:30:07Z |
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