Unique characterization of conditional distributions in nonlinear filtering

Kurtz, Thomas G.; Ocone, Daniel

doi:10.1109/cdc.1984.272100

Cited by 48 publications

(92 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Before describing it we need to recall that under very general conditions (see for instance, Kurtz and Ocone [9]), when denoting by S the state space, by F the observation space, and by P(S) the space of probability measures on S, there always exist deterministic functionals U n and U , with paths in…”

Section: General Considerations On Approximation For Filtersmentioning

confidence: 99%

Convergence in Nonlinear Filtering for Stochastic Delay Systems

Calzolari¹,

Florchinger²,

Nappo³

2007

SIAM J. Control Optim.

View full text Add to dashboard Cite

We study some approximation schemes for a nonlinear filtering problem when the state process X is the solution of a stochastic delay diffusion equation, and the observation process is a noisy function of X s for s ∈ [t − τ, t], where τ is a constant. The approximating state is given by means of an Euler discretization scheme, and the observation process is a noisy function of the approximating state.

show abstract

Section: General Considerations On Approximation For Filtersmentioning

confidence: 99%

Convergence in Nonlinear Filtering for Stochastic Delay Systems

Calzolari¹,

Florchinger²,

Nappo³

2007

SIAM J. Control Optim.

View full text Add to dashboard Cite

show abstract

“…As an example one can consider approximating and limit models like the jump model with counting observations as given by (2) and (3), for which the functionals U and U n can be computed as in (9), or like the classical diffusive model, for which the functionals U and U n are also computable as exposed in [16], for example.…”

Section: Different Kinds Of Approximationmentioning

confidence: 99%

Approximation of Nonlinear Filters for Markov Systems with Delayed Observations

Calzolari¹,

Florchinger²,

Nappo³

2006

SIAM J. Control Optim.

View full text Add to dashboard Cite

The aim of this paper is to give some approximation results for a class of nonlinear filtering problems with delay in the observation. First, we point out some general results on the approximation problem for the filter in nonlinear filtering. In particular we give a general procedure to obtain some upper bounds for the different approximations we consider. This procedure is then applied in the case of nonlinear filtering problems with delay (X, Y ), which can be represented by means of a Markov system (X,Ŷ ), in the sense that Yt =Ŷ a(t) . Finally these upper bounds are computed explicitly in the particular case of Markov jump process with counting observations.

show abstract

“…Thus, we are able to write down the filtering equation and then deal with the problem of establishing its uniqueness. To this end, we introduce the filtered martingale problem [13]. We first prove that any solution of the Kushner-Stratonovich equation provides a solution for the filtered martingale problem and then obtain uniqueness in law for the latter problem by adapting to our model a result given in [4].…”

mentioning

confidence: 99%

Multitype branching processes observing particles of a given type

Ceci

Gerardi

2005

J. Appl. Probab.

View full text Add to dashboard Cite

A multitype branching process is presented in the framework of marked trees and its structure is studied by applying the strong branching property. In particular, the Markov property and the expression for the generator are derived for the process whose components are the numbers of particles of each type. The filtering of the whole population, observing the number of particles of a given type, is discussed. Weak uniqueness for the filtering equation and a recursive structure for the linearized filtering equation are proved under a suitable assumption on the reproduction law.

show abstract

Unique characterization of conditional distributions in nonlinear filtering

Cited by 48 publications

References 2 publications

Convergence in Nonlinear Filtering for Stochastic Delay Systems

Convergence in Nonlinear Filtering for Stochastic Delay Systems

Approximation of Nonlinear Filters for Markov Systems with Delayed Observations

Multitype branching processes observing particles of a given type

Contact Info

Product

Resources

About