On the φ-asymptotic behaviour of solutions of stochastic differential equations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On the φ-asymptotic behaviour of solutions of stochastic differential equations
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| Creator |
Buldygin, V.V.
Klesov, O.I. Steinebach, J.G. Tymoshenko, O.A. |
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| 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.
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| Date |
2009-11-25T11:00:57Z
2009-11-25T11:00:57Z 2008 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/4532 519.21 |
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| Language |
en
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| Publisher |
Інститут математики НАН України
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