ISSN:0090-9491    

DOI:10.1080/17442507908833133

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

If z is the unique solution of the Itô equationand if L is a differentiable functional of the (continuous trajectories of z, then we show thatwhere μzis the function of bounded variation corresponding to the derivative ofL(z), where ø is the fundamental matrix solutiion ogf the linearized version of the zbove Itô equation, and whereis the algebra generated byw(s),s≦t.

ISSN:0090-9491    

DOI:10.1080/17442507908833134

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

A general class of parameter estimation methods for stochastic dynamical systems is studied. The class contains the least squares method, output-error methods, the maximum likelihood method and several other techniques. It is shown that the class of estimates so obtained are asymptotically normal and expressions for the resulting asymptotic covariance matrices are given. The regularity conditions that are imposed to obtain these results, are fairly weak. It is, for example, not assumed that the true system can be described within the chosen model set, and, as a consequence, the results in this paper form a part of the so-called approximate modeling approach to system identification. It is also noteworthy that arbitrary feedback from observed system outputs to observed system inputs is allowed and stationarity is not required

ISSN:0090-9491    

DOI:10.1080/17442507908833135

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442507908833136

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

In this paper an optimal stopping problem is formulated, concerned with maximizing the probability of a certain event. Necessary and sufficient conditions for existence of an optimal stopping rule are obtained. The results are then applied to a version of the discrete-time “disorder problem”

ISSN:0090-9491    

DOI:10.1080/17442507908833137

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

There already exist a fairly complete theroy for the problem of estimation and stochastic optimal control for linear distribution parameter systems, with Gaussian or non-Gaussian noise disturbance. In [8] and [12] generalizations of the familiar finite dimensional results of the kalman-bucy filter and the separtion principle are obtained using an abstract input-output Hilbert space representation for the system. However , in [8] and [12] all the input-operators are assumed to be bounded and so it does not cover the important pratical cases of control and noise on submanifolds of the spatial domain or point observations. Here we introduce unbounded system operators in the abstract iput-output Hilbert space reperesentation and thus extend all the results if [8] and [12] to allow for point observations and noise and control on submanifolds including the boundary. the theroy is illustrated by several examples

ISSN:0090-9491    

DOI:10.1080/17442507908833138

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

A robust computable approximation to the nonlinear filtering problem for a diffusion model is treated, where the system and data models are given by. The approximation (with approximation parameter h) is robust in the sense that it is locally Lipschitz continuous in the data y( °) (sup norm) uniformly inhand, ash→0, it converges to the optimal filter for the diffusion.

ISSN:0090-9491    

DOI:10.1080/17442507908833139

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

There already exists a fairly complete theory for the problems of estimation and stochastic optimal control for linear distributed parameter systems, with Gaussian or non Gaussian noise disturbance. In [8] and [12] generalizations of the familiar finite dimensional results of the Kalman-Bucy filter and the separation principle are obtained using an abstract input-output Hilbert space representation for the system. However, in [8] and [12] all the input operators are assumed to be bounded and so it does not cover the important practical cases of control and noise on submanifolds of the spatial domain or point observations. Here we introduce unbounded system operators in the abstract input-output Hilbert space representation and thus extend all the results of [8] and [12] to allow for point observations and noise and control on submanifolds including the boundary. The theory is illustrated by several examples.

ISSN:0090-9491    

DOI:10.1080/17442507908833140

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

Stochastic integrals are defined using a differential rule and the fundamental theorem of calculus. It is shown that such integrals lead to the solution of stochastic differential equations driven by a single Wiener process or square integral sample path continuous martingale

ISSN:0090-9491    

DOI:10.1080/17442507908833141

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

We establish basic results on existence and uniqueness for the solution of stochastic PDE's. We express the solution of a backward linear stochastic PDE in terms of the conditional law of a partially observed Markov diffusion process. It then follows that the adjoint forward stochastic PDE governs the evolution of the “unnormalized conditional density”

ISSN:0090-9491    

DOI:10.1080/17442507908833142

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor