TY - JOUR

T1 - Analytic diffusion processes

T2 - Definition, properties, limit theorems

AU - Ibragimov, I. A.

AU - Smorodina, N. V.

AU - Faddeev, M. M.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - Diffusion process

KW - Evolution equation

KW - Feynman integral

KW - Feynman measure

KW - Limit theorem

KW - Random process

UR - http://www.scopus.com/inward/record.url?scp=85021229905&partnerID=8YFLogxK

U2 - 10.1137/S0040585X97T988137

DO - 10.1137/S0040585X97T988137

M3 - Article

AN - SCOPUS:85021229905

VL - 61

SP - 255

EP - 276

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 2

ER -