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Teor. Veroyatnost. i Primenen., 2016, Volume 61, Issue 2, Pages 300–326 (Mi tvp5057)  

Analytic diffusion processes: definition, properties, limit theorems

I. A. Ibragimova, N. V. Smorodinab, M. M. Faddeevb

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Saint Petersburg State University

Abstract: This paper introduces the notion of an analytic diffusion process. Every process of this type is the limit of some sequence of random walks; however, the limit is understood not in the sense of convergence of measures but in the sense of convergence of generalized functions. Using the analytic diffusion processes it is possible to obtain a probabilistic approximation of solutions to Schrödinger evolution equations, whose right-hand side contains the elliptic operator with variable coefficient.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-2504.2015.1
НШ-1292.2014
Russian Foundation for Basic Research 15-01-01453_а
Saint Petersburg State University 11.38.263.2014


DOI: https://doi.org/10.4213/tvp5057

Full text: PDF file (271 kB)
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English version:
Theory of Probability and its Applications, 2017, 61:2, 255–276

Bibliographic databases:

Received: 17.03.2015

Citation: I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Analytic diffusion processes: definition, properties, limit theorems”, Teor. Veroyatnost. i Primenen., 61:2 (2016), 300–326; Theory Probab. Appl., 61:2 (2017), 255–276

Citation in format AMSBIB
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