# A Stochastic Gronwall Lemma

@inproceedings{Scheutzow2013ASG, title={A Stochastic Gronwall Lemma}, author={Michael Scheutzow}, year={2013} }

We prove a stochastic Gronwall lemma of the following type: if $Z$ is an adapted nonnegative continuous process which satisfies a linear integral inequality with an added continuous local martingale $M$ and a process $H$ on the right hand side, then for any $p \in (0,1)$ the $p$-th moment of the supremum of $Z$ is bounded by a constant $\kappa_p$ (which does not depend on $M$) times the $p$-th moment of the supremum of $H$. Our main tool is a martingale inequality which is due to D. Burkholder… CONTINUE READING

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