Lenglart's inequality explained

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

Statement

Let be a non-negative right-continuous

l{F} _{t} -adapted process and let be a non-negative right-continuous non-decreasing predictable process such that E [X(\tau)\mid l{F} _{0]\leq} E [G(\tau)\mid l{F} _{0]<} inf ty for any bounded stopping time \tau . Then

References

General sources

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