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arXiv · 1712.03157

Strong solutions of stochastic differential equations with square integrable drift

Rongrong Tian·Liang Ding·Jinlong Wei
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Abstract

We prove the existence and uniqueness of strong solutions for stochastic differential equations in which the drift coefficient is square integrable in time variable and H\"{o}lder continuous in space variable. Moreover, we prove that the unique strong solution has a continuous modification, which is $\beta$-H\"{o}lder continuous in space variable for every $\beta\in (0,1)$, and as an $L^2(\Omega\times (0,T))$ valued function, it is differentiable as well.

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Rongrong Tian, Liang Ding, Jinlong Wei. 2017-12-08. Strong solutions of stochastic differential equations with square integrable drift. https://arxiv.org/abs/1712.03157

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