Theexistenceofapathwiseuniquestrongsolutionforthestochasticdifferentialequation(S.D.E.)withPoissonjumpsinn-dimensionalspacewithoutcontinuityassumptionondriftcoefficient,whichevencanbegreaterthanlineargrowth,andwithoutLipschitzconditionondiffusioncoefficientsisobtained.ThentheexistenceofapathwisestochasticoptimalBang-Bangcontrolforaverymuchnon-linearsystemwithPoissonjumpsinn-dimensionalspaceisderived.Theresultisalsoappliedtoobtainamaximumlikelihoodestimate(MLE)ofparameterforsomecontinuous,S.D.E.withnon-Lipschitzoeffieientsinn-dimensionalspace.
