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Stochastic Gronwall inequality
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From Wikipedia, the free encyclopedia
Statement[edit]
Let be a non-negative right-continuous -adapted process. Assume that is a deterministic non-decreasing càdlàg function with and let
be a non-decreasing and càdlàg adapted process starting from . Further, let be an - local martingale with and càdlàg paths.
Assume that for all ,
where .
and define . Then the following estimates hold for and :[1][2]
-
If and is predictable, then ;
-
If and has no negative jumps, then ;
-
If then ;
It has been proven by Lenglart's inequality.[1]
References[edit]
Retrieved from "https://en.wikipedia.org/w/index.php?title=Stochastic_Gronwall_inequality&oldid=1217785928"
Categories:
●Stochastic differential equations
●Probabilistic inequalities
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