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...
Збережено в:
| Дата: | 2008 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2008
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/4532 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716429282836480 |
|---|---|
| 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. |
| 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. |
| collection | DSpace DC |
| 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.
|
| first_indexed | 2025-12-07T18:04:17Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-4532 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0321-3900 |
| language | English |
| last_indexed | 2025-12-07T18:04:17Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| 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 | 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_short | On the φ-asymptotic behaviour of solutions of stochastic differential equations |
| title_sort | on the φ-asymptotic behaviour of solutions of stochastic differential equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/4532 |
| work_keys_str_mv | AT buldyginvv ontheφasymptoticbehaviourofsolutionsofstochasticdifferentialequations AT klesovoi ontheφasymptoticbehaviourofsolutionsofstochasticdifferentialequations AT steinebachjg ontheφasymptoticbehaviourofsolutionsofstochasticdifferentialequations AT tymoshenkooa ontheφasymptoticbehaviourofsolutionsofstochasticdifferentialequations |