Zakai equation of non-linear filtering with dependent noises and unbounded observation coefficients

The author gives an existence and uniqueness result to the solution of the Zakai equation associated with a nonlinear filtering problem with dependent noises and a scalar observation process whose coefficients are unbounded. It is proved that a specified unnormalized filter solves a Zakai equation, and results of P. Cannarsa and V. Vespri (1985) are used to state a uniqueness result to the solution of that equation in convenient Holder spaces