Large deviation principle for one-dimensional SDEs with discontinuous coefficients

Daryna D. Sobolieva

Department of Probability Theory, Statistics and Actuarial Mathematics, Mechanics and Mathematics faculty, Taras Shevchenko National University of Kyiv, 6, Glushkova Prosp., Kyiv 03127, Ukraine

Abstract: We discuss the large deviation principle for one-dimensional SDEs with discontinuous coefficients. It is shown that the discontinuity of coefficients leads, in general, to the LDP asymptotics with a rate function which differs from the rate function in the standard Freidlin–Wentzell theorem.

Keywords: Large deviation principle, Varadhan lemma, Bryc formula, change of measure.

MSC: 60F10, 60H10

Language: English

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