A variational approach to nonlinear stochastic differential equations with linear multiplicative noise
2019 ◽
Vol 25
◽
pp. 71
Keyword(s):
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.
2014 ◽
Vol 417
(2)
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pp. 694-718
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1985 ◽
Vol 22
(6)
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pp. 1153-1166
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2001 ◽
Vol 44
(3)
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pp. 203-225
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2013 ◽
Vol 223
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pp. 389-400
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2011 ◽
Vol 29
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pp. 595-613
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2017 ◽
Vol 53
(2)
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pp. 503-538
2000 ◽
Vol 18
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pp. 333-345
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