Nonlinear Lévy processes and their characteristics

Neufeld, Ariel; Nutz, Marcel

doi:10.1090/tran/6656

Nonlinear Lévy processes and their characteristics
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by Ariel Neufeld and Marcel Nutz PDF

Trans. Amer. Math. Soc. 369 (2017), 69-95 Request permission

Abstract:

We develop a general construction for nonlinear Lévy processes with given characteristics. More precisely, given a set $\Theta$ of Lévy triplets, we construct a sublinear expectation on Skorohod space under which the canonical process has stationary independent increments and a nonlinear generator corresponding to the supremum of all generators of classical Lévy processes with triplets in $\Theta$. The nonlinear Lévy process yields a tractable model for Knightian uncertainty about the distribution of jumps for which expectations of Markovian functionals can be calculated by means of a partial integro-differential equation.

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