Some Solvable Classes of Filtering Problem with Ornstein-uhlenbeck Noise
نویسندگان
چکیده
This is a companion paper of Crisan et el [4]. In this article, we study a few classes of solvable models of the stochastic filtering problems with Ornstein-Uhlenbeck noise: Firstly, we study the singular linear filter with OU noise. Secondly, for nonsingular linear filtering with OU noise, we consider the limit to the classical Kalman-Bucy filter as the OU process converges to the Brownian motion. Finally, we investigate the same filtering problem when the signal is governed by a nonlinear stochastic differential equation.
منابع مشابه
On Filtering with Ornstein-Uhlenbeck Process as Noise
We consider the nonlinear filtering model with Ornstein-Uhlenbeck process as noise and obtain an analogue of the Bayes’ formula for the filter. For this we need to consider a modified model, where the instaneteneous effect h(Xt) of the signal in the usual model is replaced by ξ t = α ∫ t (t− 1 α )∨0 h(Xu) du, (where α is a large parameter). This means that there is a lingering effect of the sig...
متن کاملA Statistical Study of two Diffusion Processes on Torus and Their Applications
Diffusion Processes such as Brownian motions and Ornstein-Uhlenbeck processes are the classes of stochastic processes that have been investigated by researchers in various disciplines including biological sciences. It is usually assumed that the outcomes of these processes are laid on the Euclidean spaces. However, some data in physical, chemical and biological phenomena indicate that they cann...
متن کاملIntroducing Randomness into First-Order and Second-Order Deterministic Differential Equations
We incorporate randomness into deterministic theories and compare analytically and numerically some well-known stochastic theories: the Liouville process, the Ornstein-Uhlenbeck process, and a process that is Gaussian and exponentially time correlated Ornstein-Uhlenbeck noise . Different methods of achieving the marginal densities for correlated and uncorrelated noise are discussed. Analytical ...
متن کاملConvergence of Passive Scalars in Ornstein-uhlenbeck Flows to Kraichnan’s Model
We prove that the passive scalar field in the Ornstein-Uhlenbeck velocity field with wave-number dependent correlation times converges, in the white-noise limit, to that of Kraichnan’s model with higher spatial regularity.
متن کاملNonnegativity of solutions to the basic adjoint relationship for some diffusion processes
For a multi-dimensional diffusion process, an important problem is whether the associated basic adjoint relationship (BAR) uniquely characterizes the stationary distribution of the diffusion process. A key step in this characterization is an open problem that any solution to BAR does not change sign. This note describes the open problem precisely in the context of two classes of diffusion proce...
متن کامل