On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations with jumps

Details On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations with jumps On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations with jumps

2011-08-19

arxiv.org/abs/1108.4016v1

Mathematics

Probability

Scientific paper

We consider one-dimensional stochastic differential equations with jumps in the general case. We introduce new technics based on local time and we prove new results on pathwise uniqueness and comparison theorems. Our approach are very easy to handled and don't need any approximation approach. Similar equations without jumps were studied in the same context by \cite{Le Gall}, \cite{Ouknine} and others authors. As an application we get a new condition on the pathwise uniqueness for the solutions to stochastic differential equations driven by a symmetric stable L\'evy processes.

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