Applied Mathematics and Optimization, Vol.64, No.1, 37-69, 2011
Model Problem for Integro-Differential Zakai Equation with Discontinuous Observation Processes
The existence and uniqueness in Holder spaces of solutions of the Cauchy problem to a stochastic parabolic integro-differential equation of the order alpha a parts per thousand currency sign2 is investigated. The equation considered arises in a filtering problem with a jump signal process and a jump observation process.
Keywords:Stochastic parabolic integro-differential equations;Nonlinear filtering of jump processes;Stochastic Holder spaces