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Large deviations principles for stochastic scalar conservation laws, Probability Theory and Related Fields, to appear, preprint arXiv:0804.0997v3

By Mauro Mariani


Abstract. Large deviations principles for a family of scalar 1 + 1 dimensional conservative stochastic PDEs (viscous conservation laws) are investigated, in the limit of jointly vanishing noise and viscosity. A first large deviations principle is obtained in a space of Young measures. The associated rate functional vanishes on a wide set, the so-called set of measurevalued solutions to the limiting conservation law. A second order large deviations principle is therefore investigated, however, this can be only partially proved. The second order rate functional provides a generalization for non-convex fluxes of the functional introduced by Jensen [12] and Varadhan [21] in a stochastic particles system setting. 1

Year: 2013
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