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A Note on the Convergence of Integral Functionals of Diffusion Processes. An Application to Strong Convergence
Author(s) -
Liese F.,
Schmidt W.
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19931610121
Subject(s) - mathematics , convergence (economics) , zero (linguistics) , diffusion , sequence (biology) , diffusion process , simple (philosophy) , type (biology) , weak convergence , mathematical analysis , pure mathematics , thermodynamics , physics , computer security , computer science , economics , asset (computer security) , economic growth , ecology , linguistics , philosophy , genetics , innovation diffusion , knowledge management , epistemology , biology
Abstract For a diffusion type process d X t = d W i + a ( t, X )d t and a sequence ( f n ) of nonnegative functions necessary and sufficient conditions to the f n are established which guarantee the a.s. convergence of f n ( X t )d t to zero. This result is applied to derive simple necessary and sufficient conditions for the strong convergence of distributions of diffusion processes formulated in terms of the corresponding drift functions.