On the φ-asymptotic behaviour of solutions of stochastic differential equations
In this paper we study the a.s. asymptotic behaviour of the solution of the stochastic dfferential equation dX(t) = g(X(t))dt +σ(X(t))dW(t), X(0) = b > 0, where g and σ are positive continuous functions and W is a Wiener process. Making use of the theory of pseudo-regularly varying (PRV) function...
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| Дата: | 2008 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/4532 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the φ-asymptotic behaviour of solutions of stochastic differential equations / V.V. Buldygin, O.I. Klesov, J.G. Steinebach, O.A. Tymoshenko // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 1. — С. 11–29. — Бібліогр.: 28 назв.— англ. |
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nasplib_isofts_kiev_ua-123456789-4532 |
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Buldygin, V.V. Klesov, O.I. Steinebach, J.G. Tymoshenko, O.A. 2009-11-25T11:00:57Z 2009-11-25T11:00:57Z 2008 On the φ-asymptotic behaviour of solutions of stochastic differential equations / V.V. Buldygin, O.I. Klesov, J.G. Steinebach, O.A. Tymoshenko // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 1. — С. 11–29. — Бібліогр.: 28 назв.— англ. 0321-3900 https://nasplib.isofts.kiev.ua/handle/123456789/4532 519.21 In this paper we study the a.s. asymptotic behaviour of the solution of the stochastic dfferential equation dX(t) = g(X(t))dt +σ(X(t))dW(t), X(0) = b > 0, where g and σ are positive continuous functions and W is a Wiener process. Making use of the theory of pseudo-regularly varying (PRV) functions, we find conditions on g, σ and φ, under which φ(X(•)) can be approximated a.s. by φ(μ(•), where μ is the solution of the ordinary differential equation dμ(t) = g(μ(t))dt, μ(0) = b. As an application of these results we discuss the problem of φ-asymptotic equivalence for solutions of stochastic differential equations. This work has partially been supported by Deutsche Forschungsgemeinschaft under DFG grants 436 UKR 113/41/0-2 and 436 UKR 113/68/0-1 en Інститут математики НАН України On the φ-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 |
On the φ-asymptotic behaviour of solutions of stochastic differential equations |
| spellingShingle |
On the φ-asymptotic behaviour of solutions of stochastic differential equations Buldygin, V.V. Klesov, O.I. Steinebach, J.G. Tymoshenko, O.A. |
| title_short |
On the φ-asymptotic behaviour of solutions of stochastic differential equations |
| title_full |
On the φ-asymptotic behaviour of solutions of stochastic differential equations |
| title_fullStr |
On the φ-asymptotic behaviour of solutions of stochastic differential equations |
| title_full_unstemmed |
On the φ-asymptotic behaviour of solutions of stochastic differential equations |
| title_sort |
on the φ-asymptotic behaviour of solutions of stochastic differential equations |
| author |
Buldygin, V.V. Klesov, O.I. Steinebach, J.G. Tymoshenko, O.A. |
| author_facet |
Buldygin, V.V. Klesov, O.I. Steinebach, J.G. Tymoshenko, O.A. |
| publishDate |
2008 |
| language |
English |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
In this paper we study the a.s. asymptotic behaviour of the solution of the stochastic dfferential equation dX(t) = g(X(t))dt +σ(X(t))dW(t), X(0) = b > 0, where g and σ are positive continuous functions and W is a Wiener process. Making use of the theory of pseudo-regularly varying (PRV) functions, we find conditions on g, σ and φ, under which φ(X(•)) can be approximated a.s. by φ(μ(•), where μ is the solution of the ordinary differential equation dμ(t) = g(μ(t))dt, μ(0) = b. As an application of these results we discuss the problem of φ-asymptotic equivalence for solutions of stochastic differential equations.
|
| issn |
0321-3900 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/4532 |
| citation_txt |
On the φ-asymptotic behaviour of solutions of stochastic differential equations / V.V. Buldygin, O.I. Klesov, J.G. Steinebach, O.A. Tymoshenko // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 1. — С. 11–29. — Бібліогр.: 28 назв.— англ. |
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2025-12-07T18:04:17Z |
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