A Characterization of Measures for a Class of Continuous-Time, Partially Observable Markov Processes,
Abstract
The report concerns itself with the problem of obtaining a characterization of the measures for a class of continuous -time, partially observable Markov processes. In particular, this investigation considers processes of the diffusion type which can be described by Ito stochastic integral equations where the drift coefficients may be unbounded. The measures which are to be characterized are the conditional probability measures for the current state of the system given the entire history of the observed portion of the process. The study provides some sufficient conditions to rigorously show that the desired conditional probability measures are absolutely continuous with respect to the Lebesgue measure defined on a Euclidean space. Hence the existence of the conditional probability density is established. Then it is rigorously demonstrated that an unnormalized version of the desired conditional density can be obtained as the limit of a sequence of random functions. Subsequently, the sequences of random functions are shown to be the unique solutions to a sequence of stochastic integral equations. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1970
- Accession Number
- AD0722455
Entities
People
- Elliot Horowitz
Organizations
- University of California, Los Angeles