Filtering of Partially Observable Stochastic Processes
Aleksandar Zatezalo
Doctor of Philosophy in Mathematics (Industrial and Applied emphasis), June
1998
Call Number: MnU-D 98-158
Filtering equations are derived for two different cases of partially observable
stochastic processes; finite-state time-nonhomogeneous cadlag Markov Processes
and diffusion processes.
For the first case, the filtering equations are new and are natural generalization
of already known filtering equations for finite-state time-homeogeneous cadlag
Markov processes. We also developed a new method of derivation called "a direct
approach."
A similar method is applied in the second case for already known results in
Sobolev spaces. Characteristics of the method are its simplicity, application
of Ito's formula, integration by parts, and use of the theory of ordinary differential
equations in the first case and partial differential equations in the second
case, respectively.
Research supported by the Minnesota Center for Industrial
Mathematics (MCIM)
