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

\mathcal_t

adapted process In the study of stochastic processes, an adapted process (also referred to as a non-anticipating or non-anticipative process) is one that cannot "see into the future". An informal interpretation is that ''X'' is adapted if and only if, for every rea ...

and let be a non-negative right-continuous non-decreasing predictable process such that

\infty

for any bounded stopping time

\tau

. Then (i)

\mathbb\left(\sup_G(t)\geq d\,\Big\vert\mathcal_0\right).

(ii)

\text c_p:=\frac

Notes

: 1.See ''Théorème'' I and ''Corollaire ''II of

Bibliography

* * * * * {{DEFAULTSORT:Lenglart's inequality Stochastic differential equations Articles containing proofs Probabilistic inequalities