caa a22 4500 463177185 CHVBK 20180406164828.0 cr unu---uuuuu 170326e20071001xx s 000 0 eng 10.1007/s10986-007-0025-7 doi (NATIONALLICENCE)springer-10.1007/s10986-007-0025-7 PRV property and the ϕ -asymptotic behavior of solutions of stochastic differential equations [Elektronische Daten] [V. Buldygin, O. Klesov, J. Steinebach] In this paper, we investigate the a.s. asymptotic behavior of the solution of the stochastic differential equation dX(t) = g(X(t)) dt + σ(X(t))dW(t), X(0) ≢ 1, where g(·) and σ(·) are positive continuous functions, and W(·) is a standard Wiener process. By means of the theory of PRV functions we find conditions on g(·), σ(·), and ϕ(·) under which ϕ(X(·)) may be approximated a.s. by ϕ(μ(·)) on {X(t) → ∞}, where μ(·) is the solution of the ordinary differential equation dμ(t) = g(μ(t)) dt with μ(0) = 1. Springer Science+Business Media, Inc., 2007 stochastic differential equation nationallicence asymptotic behavior of solutions nationallicence pseudo-regulary varying function nationallicence Buldygin V. Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine, pr. Peremogy, 37, 03056, Kyiv, Ukraine aut Klesov O. Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine, pr. Peremogy, 37, 03056, Kyiv, Ukraine aut Steinebach J. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-50931, Köln, Germany aut Lithuanian Mathematical Journal Springer US 47/4(2007-10-01), 361-378 0363-1672 47:4<361 2007 47 10986 https://doi.org/10.1007/s10986-007-0025-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10986-007-0025-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Buldygin V. Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine, pr. Peremogy, 37, 03056, Kyiv, Ukraine aut NATIONALLICENCE 700 1- Klesov O. Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine, pr. Peremogy, 37, 03056, Kyiv, Ukraine aut NATIONALLICENCE 700 1- Steinebach J. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-50931, Köln, Germany aut NATIONALLICENCE 773 0- Lithuanian Mathematical Journal Springer US 47/4(2007-10-01), 361-378 0363-1672 47:4<361 2007 47 10986 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer