This website uses third party cookies to improve your experience. If you continue browsing or close this notice, you will accept their use.

Strong solutions to monotone semilinear SPDEs with semimartingale noise

19 July 2018 at 12:00 PM - 3:00 PM

Room 209, Campus on 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.)