Existence for nonlinear finite dimensional stochastic differential equations of subgradient type

Viorel Barbu

doi:10.3934/mcrf.2018020

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2018, Volume 8, Issue 3&4: 501-508. Doi: 10.3934/mcrf.2018020

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Existence for nonlinear finite dimensional stochastic differential equations of subgradient type

Viorel Barbu

Octav Mayer Institute of Mathematics of Romanian Academy, Iaşi, Romania

Received: September 2017

Revised: January 2018

Published: September 2018

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Abstract

One proves via variational techniques the existence and uniqueness of a strong solution to the stochastic differential equation $dX+{\partial} {\varphi} (t,X)dt\ni \sum\limits^N_{i = 1}σ_i(X)d{β}_i,\ X(0) = x,$ where ${\partial}{\varphi} :{\mathbb{R}}^d\to2^{{\mathbb{R}}^d}$ is the subdifferential of a convex function ${\varphi}:{\mathbb{R}}^d\to{\mathbb{R}}$ and $σ_i∈ L({\mathbb{R}}^d,{\mathbb{R}}^d)$, $1≤ d<{∞}$.

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Mathematics Subject Classification: Primary: 60H15, 47H05, 49K15; Secondary: 47J05, 47N10.

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References

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