Lenglart's inequality

In the mathematical theory of probability, Lenglart's inequality was proved by Èrik Lenglart in 1977.[1] Later slight modifications are also called Lenglart's inequality.

Statement

Let X be a non-negative right-continuous -adapted process and let G be a non-negative right-continuous non-decreasing predictable process such that for any bounded stopping time . Then

References

Citations

  1. Lenglart 1977, Théorème I and Corollaire II, pp. 171−179

General sources

  • Geiss, Sarah; Scheutzow, Michael (2021). "Sharpness of Lenglart's domination inequality and a sharp monotone version". Electronic Communications in Probability. 26: 1–8. arXiv:2101.10884. doi:10.1214/21-ECP413. S2CID 231709277.
  • Lenglart, Érik (1977). "Relation de domination entre deux processus". Annales de l'Institut Henri Poincaré B. 13 (2): 171−179.
  • Mehri, Sima; Scheutzow, Michael (2021). "A stochastic Gronwall lemma and well-posedness of path-dependent SDEs driven by martingale noise". Latin Americal Journal of Probability and Mathematical Statistics. 18: 193−209. doi:10.30757/ALEA.v18-09. S2CID 201660248.
  • Ren, Yaofeng; Schen, Jing (2012). "A note on the domination inequalities and their applications". Statist. Probab. Lett. 82 (6): 1160−1168. doi:10.1016/j.spl.2012.03.002.
  • Revuz, Daniel; Yor, Marc (1999). Continuous Martingales and Brownian Motion. Berlin: Springer. ISBN 3-540-64325-7.


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