摘要:

In this paper, a partially observed linear system is considered with arbitrary non-Gaussian initial conditions and the corresponding (nonlinear) filtering problem is investigated. An explicit formula is obtained for the conditional expectation of an arbitrary function of the current state given past observations; a set of sufficient statistics is shown to exist which are recursively computable as outputs of a finite-dimensional dynamical system. The basic results are specialized to purely complex exponentials and to indicator functions of Bore1 sets, and yield formulae for the conditional characteristic function and probability law of the current state given past observations. A special case when some covariance matrix is invertible, is also studied and a sharpening of the basic results is obtained as the existence and form of a conditional density is established. The method of analysis is probabilistic and relies on Girsanov's Theorem, basic results in linear filtering, theory and some easy facts for Gaussian random variables.

ISSN:0090-9491    

DOI:10.1080/17442508608833364

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

A natural adaptive Linear Quadratic Regulator is studied. The optimal control is shown to be the conditional expectation, given the observations, of the linear quadratic control computed assuming the true parameter were known. Moreover this control is stabilizing. The new ingredient that makes these results possible is the introduction of the concept of entropy into this setting.

ISSN:0090-9491    

DOI:10.1080/17442508608833365

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

This paper deals with a nonlinear filtering approach to the problem of intensity parameter estimation of a doubly stochastic Poisson process, driven by an unob‐ servable Markov process. We present a method for the evaluation of the conditional likelihood ratio, given the observations of one path of the point process. By the methodsof Ibragimov, Khasminskii and Kutoyants we investigate the asymptotic properties of the corresponding maximum likelihood estimator. In the ergodic case consistency, asymptotic normality, convergence of the moments and asymptotic efficiency are established.

ISSN:0090-9491    

DOI:10.1080/17442508608833366

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

The paper treats a number of problems in nonlinear filtering theory when the signal process is xs:(), a “near” diffusion, and the observation noise is of wide bandwidth (correlated or not with xs()). Natural modifications of the optimal filters for the classical (diffusion) case are described, and robustness and weak convergence results proved. Often the weak convergence is in an infinite dimensional setting, since the basic process is measure valued. These filters are not actually optimal for the “physical” process, and their value depends on the use to which they are put. It is shown that they are actually nearly “optimal” with respect to a wide variety of comparison processors. We also treat the normalized (Césaro) errors (for the “approximate” filters) over an infinite time interval, and show that their distributions are close (for wide bandwidth observation noise) to those obtained if the system were a standard diffusion and the optimal filter used. This is particularly important if the system is in operation for a long time period.

ISSN:0090-9491    

DOI:10.1080/17442508608833367

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

A quasimartingale is a right-continuous process with bounded conditional mean variation. If a process is a quasimartingale then it is a semimartingale; in this paper sufficient conditions are presented under which the converse is true.

ISSN:0090-9491    

DOI:10.1080/17442508608833368

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

Let ue(x, t) denote the weak solution to a parabolic PDE whose inputs and coefficients are wide bandwidth stochastic processes, and the bandwidth goes to as e-->0. Under known conditions, ue(•,•) converges weakly to a certain parabolic PDE driven by a (finite dimensional or cylindrical) Wiener process. A key problem in applications concerns the behavior of ue(x, t) for large time and small e . This is, perhaps, the main stability problem for such stochastic PDEs. We show (under appropriate conditions) that the tail of ueis (in the sense of distributions) close to a stationary solution of the limit (Wiener process driven) system, for small e. The methods are purely probabilistic, and depend on interpretations of the solutions ue(•,•) as functionals of certain diffusions with wide bandwidth coefficients. No PDE methods are used.

ISSN:0090-9491    

DOI:10.1080/17442508608833369

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

We present a method for detecting changes in the AR parameters of an ARMA process with arbitrarily time varying MA parameters. Assuming that a collection of observations and a set of nominal time invariant AR parameters are given, we test if the observations are generated by the nominal AR parameters or by a different set of time invariant AR parameters. The detection method is derived by using a local asymptotic approach and it is based on an estimation procedure which was shown to be consistent under nonstationarities.

ISSN:0090-9491    

DOI:10.1080/17442508608833370

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508608833363

出版商:Gordon and Breach Science Publishers    

年代:1986

数据来源: Taylor