Abstract
We study the rate of convergence of the processξ(tT)/√T to the processw(t)/σ asT → ∞, whereξ(t) is a solution of the stochastic differential equationdξ(t)=a(ξ(t))dt+σ(ξ(t))dw(t)
This is a preview of subscription content, log in via an institution to check access.
References
G. L. Kulinich, “Asymptotic normality of the distributions of solutions of a stochastic diffusion equation,”Ukr. Mat. Zh.,20, No. 3, 396–400 (1968).
I. I. Gikhman and A. V. Skorokhod,Stochastic Differential Equations [in Russian], Naukova Dumka, Kiev (1968).
G. L. Kulinich, “On the asymptotic behavior of the distributions of functionals of the form∫ t0 g(ξ,(s))ds for diffusion processes,”Teor. Ver. Mat. Statist., Issue 8, 99–105 (1973).
G. L. Kulinich, “Limit distributions of integral-type functionals of unstable diffusion processes,”Teor. Ver. Mat. Statist., Issue 11, 81–85 (1974).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1424–1427, October, 1994.
Rights and permissions
About this article
Cite this article
Mynbaeva, G.U. On the rate of convergence of an unstable solution of a stochastic differential equation. Ukr Math J 46, 1573–1577 (1994). https://doi.org/10.1007/BF01066105
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01066105