FREIDLIN-WENTZELL LDP IN PATH SPACE FOR MCKEAN-VLASOV EQUATIONS AND THE FUNCTIONAL ITERATED LOGARITHM LAW

被引：65

作者：

dos Reis, Goncalo ^{[1
]}

Salkeld, William ^{[1
]}

Tugaut, Julian ^{[2
]}

机构：

[1] Univ Edinburgh, Sch Math, Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Midlothian, Scotland

[2] Univ Jean Monnet, Inst Camille Jordan, 23 Rue Docteur Paul Michelon, F-42023 St Etienne, France

来源：

ANNALS OF APPLIED PROBABILITY | 2019年 / 29卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

McKean-Vlasov equations; large deviations principle; path-space; Holder topologies; superlinear growth; functional Strassen law; LARGE DEVIATIONS; PROPAGATION; THEOREM; LIMIT;

D O I：

10.1214/18-AAP1416

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We show two Freidlin-Wentzell-type Large Deviations Principles (LDP) in path space topologies (uniform and Holder) for the solution process of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) using techniques which directly address the presence of the law in the coefficients and altogether avoiding decoupling arguments or limits of particle systems. We provide existence and uniqueness results along with several properties for a class of MV-SDEs having random coefficients and drifts of superlinear growth. As an application of our results, we establish a functional Strassen-type result (law of iterated logarithm) for the solution process of a MV-SDE.

引用

页码：1487 / 1540

页数：54

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