Abstract

We consider one-dimensional stochastic differential equations of the Stratonovich type: dX_t=\sum_i\sigma_i(t,\omega,X_t)\circ dZ^i_t+ \sum_kh_k(t,\omega,X_t)dA^k_t where Z(i) are continuous semimartingales, and A(k) are continuous finite variation processes. We extend the definition of the Fisk-Stratonovich integral for a large class of coefficients sigma(i), and under suitable conditions we prove existence and uniqueness for that equation.