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Stochastic Viability and Comparison Theorems for Mixed Stochastic Differential Equations |
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| Authors: | Alexander?Melnikov Yuliya?Mishura |
| Institution: | 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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