Reciprocal Property for a Class of Anticipating Stochastic Differential Equations

#### A. Alabert, M.A. Marmolejo

1999, v.5, Issue 3, 331-356

ABSTRACT

We study a class of one-dimensional stochastic differential equations with boundary conditions by means of a change of variables that reduces the diffusion coefficient to a constant. We obtain a representation of the type $X_t=G(t,Y_t)$, where $Y$ is the solution of the simpler equation. This representation is used to show several properties of the original equation. In particular, our main result is a characterization of the coefficients for which the solution process satisfies a suitable Markov-type property, namely, the reciprocal property.

Keywords: anticipating stochastic differential equations,reciprocal processes