Representation of solutions to sticky stochastic differential equations

Abstract

In this paper, we study a representation for the solutions to sticky stochastic differential equations driven by a continuous process. The involved stochastic integral is interpreted in three different ways. Namely, we deal with Young integral defined by the fractional calculus, and the forward and symmetric integrals in the Russo and Vallois sense. The representation obtained in this paper depends on the amount of time spent by the solution at zero. Hence, we obtain the uniqueness for the solution among the processes that spend zero time at [Formula: see text].