Volume 25, 2019
|Number of page(s)||16|
|Published online||27 November 2019|
A variational approach to nonlinear stochastic differential equations with linear multiplicative noise
Octav Mayer Institute of Mathematics of Romanian Academy,
* Corresponding author: email@example.com
Accepted: 13 November 2018
One introduces a new concept of generalized solution for nonlinear infinite dimensional stochastic differential equations of subgradient type driven by linear multiplicative Wiener processes. This is defined as solution of a stochastic convex optimization problem derived from the Brezis-Ekeland variational principle. Under specific conditions on nonlinearity, one proves the existence and uniqueness of a variational solution which is also a strong solution in some significant situations. Applications to the existence of stochastic total variational flow and to stochastic parabolic equations with mild nonlinearity are given.
Mathematics Subject Classification: 60H15 / 47H05 / 47J05
Key words: Wiener process / convex function / subdifferential / stochastic total variation flow
© EDP Sciences, SMAI 2019
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