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періодичних видань НАН України
PRV property and the asymptotic behaviour of solutions of stochastic differential equations
Репозиторій DSpace/Manakin
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PRV property and the asymptotic behaviour of solutions of stochastic differential equations
УДК:
519.21
Посилання:
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.
Підтримка:
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.
Дата:
2005
Переглядів:
1406
Завантажень:
787
Анотація:
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.
