Commutative and noncommutarive stochastic calculus : theory and applications

Abstract : My PhD work is composed of two parts, the first part is dedicated to the discrete-time stochastic analysis for obtuse random walks as to the second part, it is linked to free probability. In the first part, we present a construction of the stochastic integral of predictable square-integrable processes and the associated multiple stochastic integrals ofsymmetric functions on Nn (n_1), with respect to a normal martingale.[...] In a second step, we revisited thedescription of the marginal distribution of the Brownian motion on the large-size complex linear group. Precisely, let (Z(d)t )t_0 be a Brownian motion on GL(d,C) and consider nt the limit as d !¥ of the distribution of (Z(d)t/d)⋆Z(d)t/d with respect to E×tr.
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Tarek Hamdi. Commutative and noncommutarive stochastic calculus : theory and applications. General Mathematics [math.GM]. Université de Franche-Comté, 2013. English. ⟨NNT : 2013BESA2015⟩. ⟨tel-01141703⟩

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