On large deviations for small noise It\^o processes

Alberto Chiarini; Markus Fischer

doi:10.1239/aap/1418396246

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arXiv · 1212.3223

On large deviations for small noise It\^o processes

Alberto Chiarini·Markus Fischer

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Abstract

The large deviation principle in the small noise limit is derived for solutions of possibly degenerate It\^o stochastic differential equations with predictable coefficients, which may depend also 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.

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Alberto Chiarini, Markus Fischer. 2012-12-13. On large deviations for small noise It\^o processes. https://doi.org/10.1239/aap%2F1418396246

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