# American Institute of Mathematical Sciences

September & December  2018, 8(3&4): 501-508. doi: 10.3934/mcrf.2018020

## Existence for nonlinear finite dimensional stochastic differential equations of subgradient type

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

This paper is dedicated to Professor Jiongmin Yong on the occasion of his 60th birthday

Received  September 2017 Revised  January 2018 Published  September 2018

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 $σ_i∈ L({\mathbb{R}}^d,{\mathbb{R}}^d)$, $1≤ d<{∞}$.

Citation: Viorel Barbu. Existence for nonlinear finite dimensional stochastic differential equations of subgradient type. Mathematical Control & Related Fields, 2018, 8 (3&4) : 501-508. doi: 10.3934/mcrf.2018020
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This paper is dedicated to Professor Jiongmin Yong on the occasion of his 60th birthday

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