Stochastic differential equations with random coefficients (Q1363405)

Let \[ X_t=X_0 +\int^t_0 b(X_s)d A_s+\int^t_0 \sigma(X_s) \circ dM_s, \tag{1} \] where \(X_0\) is a given random variable, \(b,\sigma\) are random functions, \(Z_t\), \(t\in[0,1]\), is a continuous semimartingale which has a canonical decomposition \(Z_t= M_t+A_t\), be a one-dimensional stochastic differential equation in the Stratonovich sense. The problem of the existence and uniqueness of a solution of (1) is considered. It is also established the existence and uniqueness of the solution for two cases of multidimensional Stratonovich equations.