Large deviation problem for some parabolic itǒ equations | Zendy

Chow PaoLiu | Zendy

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Large deviation problem for some parabolic itǒ equations

Author(s) -

Chow PaoLiu

Publication year - 1992

Publication title -

communications on pure and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.12

H-Index - 115

eISSN - 1097-0312

pISSN - 0010-3640

DOI - 10.1002/cpa.3160450105

Subject(s) - mathematics , rate function , multiplicative function , mathematical analysis , large deviations theory , hilbert space , space (punctuation) , parabolic partial differential equation , function (biology) , type (biology) , multiplicative noise , class (philosophy) , partial differential equation , statistics , ecology , linguistics , philosophy , signal transfer function , digital signal processing , evolutionary biology , artificial intelligence , computer science , analog signal , electrical engineering , biology , engineering

The large deviation problem of Wentzell‐Freidlin type is considered for a class of semilinear parabolic equations perturbed by a small multiplicative noise. In a Hilbert space setting, it is proved that, under suitable conditions, the associated family of solution measures, depending on a small parameter, obeys the large deviation principle with respect to a certain rate function.

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