A STUDY OF A ONE-DIMENSIONAL BILINEAR DIFFERENTIAL MODEL
FOR STOCHASTIC PROCESSES
Abstract: This paper is concerned with a study of a one-dimensional bilinear differential
model for stochastic processes in continuous time. We provide conditions for second-order
and strict-sense stationarities of the state process. We obtain a linear representation
of the state process, derive the optimal linear filter, and investigate its asymptotic
behaviour. We consider the problem of parameter estimation for the autonomous
version of the model. By the use of the quadratic variation of the process we compute
the diffusion coefficient parameters. In the reduced model, under the additional
assumption that the parameters of the diffusion coefficient are known, we use the
maximum likelihood method and the method of moments, in order to estimate the drift
coefficient parameters. We prove consistency and asymptotic normality of the estimates.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -