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
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