Stochastic viability and comparison theorems for mixed stochastic differential equations

Alexander Melnikov, Yuliya Mishura, Georgiy Shevchenko

Published 2012-11-08Version 1

For a mixed stochastic differential equation containing both Wiener process and a H\"older continuous process with exponent $\gamma>1/2$, 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.