Stochastic viability and comparison theorems for mixed stochastic   differential equations
  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. 
Alexander Melnikov and Yuliya Mishura and Georgiy Shevchenko
math.PR