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2006 Convex Concentration Inequalities and Forward-Backward Stochastic Calculus
Thierry Klein, Yutao Ma, Nicolas Privault
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Electron. J. Probab. 11: 486-512 (2006). DOI: 10.1214/EJP.v11-332


Given $(M_t)_{t\in \mathbb{R}_+}$ and $(M^*_t)_{t\in \mathbb{R}_+}$ respectively a forward and a backward martingale with jumps and continuous parts, we prove that $E[\phi (M_t+M^*_t)]$ is non-increasing in $t$ when $\phi$ is a convex function, provided the local characteristics of $(M_t)_{t\in \mathbb{R}_+}$ and $(M^*_t)_{t\in \mathbb{R}_+}$ satisfy some comparison inequalities. We deduce convex concentration inequalities and deviation bounds for random variables admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component


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Thierry Klein. Yutao Ma. Nicolas Privault. "Convex Concentration Inequalities and Forward-Backward Stochastic Calculus." Electron. J. Probab. 11 486 - 512, 2006.


Accepted: 7 July 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1112.60034
MathSciNet: MR2242653
Digital Object Identifier: 10.1214/EJP.v11-332

Primary: 60F99
Secondary: ‎39B62 , 60F10 , 60H07

Keywords: Brownian motion , Clark formula , Convex concentration inequalities , Deviation inequalities , forward-backward stochastic calculus , Jump processes

Vol.11 • 2006
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