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.
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References
A. V. Skorokhod,Investigations in the Theory of Stochastic Processes [in Russian], Kiev University, Kiev (1991).
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S. I. Pisanets, “Limit theorems for the diffusion-type processes inR m,”Teor. Veroyatn. Primen., No. 3, 537–606 (1981).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1371–1378, October, 1993.
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Pisanets, S.I. Limit theorems for diffusion-type processes inR m . Ukr Math J 45, 1539–1547 (1993). https://doi.org/10.1007/BF01571088
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DOI: https://doi.org/10.1007/BF01571088