A Stochastic Gronwall Lemma

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

    Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

    Citations

    Publications citing this paper.
    SHOWING 1-10 OF 23 CITATIONS

    A discrete stochastic Gronwall lemma

    VIEW 6 EXCERPTS
    CITES BACKGROUND & METHODS

    Strong Uniqueness of Degenerate SDEs with H\"older diffusion coefficients

    VIEW 2 EXCERPTS
    CITES BACKGROUND
    HIGHLY INFLUENCED

    Well-posedness of distribution dependent SDEs with singular drifts.

    VIEW 3 EXCERPTS
    CITES BACKGROUND
    HIGHLY INFLUENCED

    Continuity properties of the semi-group and its integral kernel in non-relativistic QED

    VIEW 3 EXCERPTS
    CITES METHODS
    HIGHLY INFLUENCED

    References

    Publications referenced by this paper.
    SHOWING 1-4 OF 4 REFERENCES

    Existence and uniqueness of solutions of stochastic functional differential equations , Random Oper

    • M. Renesse, M. Scheutzow
    • Stoch . Equ .
    • 2010