Abstract
For a sequence of stochastic equations of diffusion type, conditions that are close to necessary and sufficient ones are established for the weak convergence of measures\(\mu _{(\xi ^{(n)} ,w)} \),n=1, ... , associated with the solutions, to the limiting measure\( \mu _{(\xi ^{(0)} ,w)} \). The conditions under which the weak convergence of the solutions of stochastic equations implies their strong convergence are established as well.
Similar content being viewed by others
References
A. V. Skorokhod,Investigations in the Theory of Stochastic Processes [in Russian], Kiev University, Kiev (1991).
I. I. Gikhman and A. V. Skorokhod,Theory of Stochastic Processes [in Russian], Nauka, Moscow (1971–1975).
I. I. Gikhman and A. V. Skorokhod,Controlled Stochastic Processes [in Russian], Naukova Dumka, Kiev (1976).
S. I. Pisanets, “Limit theorems for the diffusion-type processes inR m,”Teor. Veroyatn. Primen., No. 3, 537–606 (1981).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1371–1378, October, 1993.
Rights and permissions
About this article
Cite this article
Pisanets, S.I. Limit theorems for diffusion-type processes inR m . Ukr Math J 45, 1539–1547 (1993). https://doi.org/10.1007/BF01571088
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01571088