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On Large Deviations for Small Noise Itô Processes

Part of: Stochastic analysis Markov processes Limit theorems Functional-differential and differential-difference equations

Published online by Cambridge University Press:  22 February 2016

Alberto Chiarini  and
Markus Fischer
Alberto Chiarini*
Affiliation:
Technische Universität Berlin
Markus Fischer*
Affiliation:
Università di Padova
*
∗ Postal address: Department of Mathematics, Technische Universität Berlin, Straβe des 17. Juni 136, 10623 Berlin, Germany. Email address: chiarini@math.tu-berlin.de
∗∗ Postal address: Department of Mathematics, Università di Padova, via Trieste 63, 35121 Padova, Italy. Email address: fischer@math.unipd.it
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Abstract

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The large deviation principle in the small noise limit is derived for solutions of possibly degenerate Itô stochastic differential equations with predictable coefficients, which may also depend on the large deviation parameter. The result is established under mild assumptions using the Dupuis-Ellis weak convergence approach. Applications to certain systems with memory and to positive diffusions with square-root-like dispersion coefficient are included.

Keywords

Large deviationItô processstochastic differential equationFreidlin-Wentzell estimatetime delayCIR processweak convergence

MSC classification

Primary: 60F10: Large deviations 60H10: Stochastic ordinary differential equations
Secondary: 60J60: Diffusion processes 34K50: Stochastic functional-differential equations

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 46 , Issue 4 , December 2014 , pp. 1126 - 1147
Copyright
© Applied Probability Trust 

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