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Stochastic Viability and Comparison Theorems for Mixed Stochastic Differential Equations

Authors:	Alexander?Melnikov,Yuliya?Mishura,Georgiy?Shevchenko author-information" > author-information__contact u-icon-before" > mailto:zhora@univ.kiev.ua" title=" zhora@univ.kiev.ua" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	1.Department of Mathematical and Statistical Sciences,University of Alberta,Edmonton,Canada;2.Faculty of Mechanics and Mathematics, Department of Probability, Statistics and Actuarial Mathematics,Kyiv National Taras Shevchenko University,Kyiv,Ukraine

Abstract:	For a mixed stochastic differential equation containing both Wiener process and a Hölder continuous process with exponent γ?>?1/2, we prove a stochastic viability theorem. As a consequence, we get a result about positivity of solution and a pathwise comparison theorem. An application to option price estimation is given.

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