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math.PR2015
Combining losing games into a winning game
Bruno Rémillard, Jean Vaillancourt
Parrondo's paradox is extended to regime switching random walks in random environments. The paradoxical behavior of the resulting random walk is explained by the effect of the rand…
math.PR2007
Malliavin calculus and Clark-Ocone formula for functionals of a square-integrable Lévy process
Jean-François Renaud, Bruno Rémillard
In this paper, we construct a Malliavin derivative for functionals of square-integrable Lévy processes and derive a Clark-Ocone formula. The Malliavin derivative is defined via cha…