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Article Dans Une Revue Stochastics: An International Journal of Probability and Stochastic Processes Année : 2013

Convex comparison inequalities for non-Markovian stochastic integrals

Résumé

We derive convex comparison inequalities for stochastic integrals of the form integral(T)(0)sigma(t)*d (B) over cap (t) and integral(T)(0)sigma(t)dB(t), where 0 <= sigma(t)* <= sigma(t) are adapted processes with respect to the filtration generated by a standard Brownian motion (B-t)(t is an element of[0,T]), and ((B) over cap (t))(t is an element of[0,T]) is an independent Brownian motion. Our method uses forward-backward stochastic integration and the Malliavin calculus, and is also applied to jump-diffusion processes.
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Dates et versions

hal-00879513 , version 1 (04-11-2013)

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Jean-Christophe Breton, Benjamin Laquerrière, Nicolas Privault. Convex comparison inequalities for non-Markovian stochastic integrals. Stochastics: An International Journal of Probability and Stochastic Processes, 2013, 85 (5), pp.789-806. ⟨10.1080/17442508.2012.659666⟩. ⟨hal-00879513⟩
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