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math.PR2017★ 1 cited
Stochastic representation of tau functions of Korteweg-de Vries equation
Michèle Thieullen, Alexis Vigot
In this paper we express tau functions for the Korteweg de Vries (KdV) equation, as Laplace transforms of iterated Skorohod integrals. Our main tool is the notion of Fredholm deter…
math.PR2017
Iterated stochastic processes : simulation and relationship with high order partial differential equations
Michèle Thieullen, Alexis Vigot
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated proc…