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May 2018 A variational approach to dissipative SPDEs with singular drift
Carlo Marinelli, Luca Scarpa
Ann. Probab. 46(3): 1455-1497 (May 2018). DOI: 10.1214/17-AOP1207


We prove global well-posedness for a class of dissipative semilinear stochastic evolution equations with singular drift and multiplicative Wiener noise. In particular, the nonlinear term in the drift is the superposition operator associated to a maximal monotone graph everywhere defined on the real line, on which neither continuity nor growth assumptions are imposed. The hypotheses on the diffusion coefficient are also very general, in the sense that the noise does not need to take values in spaces of continuous, or bounded, functions in space and time. Our approach combines variational techniques with a priori estimates, both pathwise and in expectation, on solutions to regularized equations.


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Carlo Marinelli. Luca Scarpa. "A variational approach to dissipative SPDEs with singular drift." Ann. Probab. 46 (3) 1455 - 1497, May 2018.


Received: 1 April 2016; Revised: 1 March 2017; Published: May 2018
First available in Project Euclid: 12 April 2018

zbMATH: 06894779
MathSciNet: MR3785593
Digital Object Identifier: 10.1214/17-AOP1207

Primary: 46N30 , 47H06 , 60H15

Keywords: monotone operators , Multiplicative noise , Singular drift , stochastic evolution equations , variational approach , well-posedness

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.46 • No. 3 • May 2018
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