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Strong solutions to monotone semilinear SPDEs with semimartingale noise

19 luglio 2018 ore 12:00 - 15:00

Aula 209, Sede di Viale Romania, 32

Speaker: Carlo Marinelli , University College London

Abstract: We prove existence and uniqueness of strong solutions to a class of semilinear stochastic evolution equations driven by general Hilbertian semimartingales, with drift equal to the sum of a linear maximal monotone operator in variational form and of the superposition operator associated to a random time-dependent monotone function defined on the whole real line. Such a function is only assumed to satisfy a very mild symmetry-like condition, but its rate of growth towards infinity can be arbitrary. Moreover, the noise is of multiplicative type and can be path-dependent. The solution is obtained via a priori estimates on solutions to regularized equations, interpreted both as stochastic equations as well as deterministic equations with random coefficients, and ensuing compactness properties. A key role is played by an infinite-dimensional Doob-type inequality due to Metivier and Pellaumail. (Joint work with Luca Scarpa.)