Marinelli, Carlo;
Scarpa, Luca;
(2022)
Well-Posedness of Monotone Semilinear SPDEs with Semimartingale Noise.
In: Donati-Martin, C and Lejay, A and Rouault, A, (eds.)
Séminaire de Probabilités LI.
(pp. 259-301).
Springer, Cham: Cham, Switzerland.
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Abstract
We prove existence and uniqueness of strong solutions for a class of semilinear stochastic evolution equations driven by general Hilbert space-valued semimartingales, with drift equal to the sum of a linear maximal monotone operator in variational form and 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 Métivier and Pellaumail.
Type: | Book chapter |
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Title: | Well-Posedness of Monotone Semilinear SPDEs with Semimartingale Noise |
ISBN-13: | 978-3-030-96408-5 |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1007/978-3-030-96409-2_9 |
Publisher version: | https://doi.org/10.1007/978-3-030-96409-2_9 |
Language: | English |
Additional information: | This version is the author-accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
URI: | https://discovery.ucl.ac.uk/id/eprint/10189729 |
1. | United Kingdom | 2 |
2. | United States | 2 |
3. | China | 2 |
4. | Russian Federation | 1 |
5. | Germany | 1 |
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