On semimartingale local time inequalities and applications in SDE's

Details On semimartingale local time inequalities and applications in SDE's On semimartingale local time inequalities and applications in SDE's

2011-08-19

arxiv.org/abs/1108.4003v2

Mathematics

Probability

Scientific paper

Using the balayage formula, we prove an inequality between the measures associated to local times of semimartingales. Our result extends the "comparison theorem of local times" of Ouknine $(1988)$, which is useful in the study of stochastic differential equations. The inequality presented in this paper covers the discontinuous case. Moreover, we study the pathwise uniqueness of some stochastic differential equations involving local time of unknown process.

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