摘要:

Let {Zttε [0,1]×[0,1]} be a two-parameter random field with stationary, independent increments. A stochastic integral representation is given for all square-integrable random variables adapted to the sigma fields of Zt.

ISSN:0090-9491    

DOI:10.1080/17442508308833277

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

The standard existence and uniqueness theorem for stochastic differential equations requires Lipschitz condition of the coefficients. In this paper, we extend these results to the case in which the coefficients are not required to be Lipschitz continuous, instead they only satisfy a ‘weak’ type of Lipschitz condition.

ISSN:0090-9491    

DOI:10.1080/17442508308833278

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

Pour un processus progressif relatif a une filtration continue a droite, la fonction qui a chaque temps d'arrêt associe I'espérance mathematique de la variable aleatoire correspondante atteint sonminimum, dès qu'elle est semi-continue inferieurement le long des suites monotones,ou seulement le long des suites croissantes si en plus le processus est presque surement a trajectoires semi-continues inferieurement a droite.

ISSN:0090-9491    

DOI:10.1080/17442508308833279

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

In this paper, we investigate the identification problem of linear system theory from the viewpoint of nonlinear filtering. Following the work of Brockett and Mitter, one associates in a natural way a certain (infinite dimensional) Lie algebra of differential operators known as the estimation algebra of the problem. For the identification problem the estimation algebra is a subalgebra of a current algebra. In this paper we study questions of representation and integrability of current algebras as they impinge upon the identification problem. A Wei-Norman type procedure for the associated Cauchy problem is developed which reveals a sequence of functionals of the observations that play the role of joint sufficient statistics for the identification problem.

ISSN:0090-9491    

DOI:10.1080/17442508308833280

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

Existence of optimal controls for partially observed diffusions is established for a suitably defined class of admissible controls

ISSN:0090-9491    

DOI:10.1080/17442508308833281

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

It is shown that mean square stability of a class of nonlinear stochastic evolution equations is equivalent to that of a linear stochastic evolution equation provided noise terms in the former are dominated by that of the latter. This generalizes Morozan's result concerning the stochastic dserential equation of Lur'e type to a much wider class of stochastic evolution equations in Hilbert space. Two examples are given to illustrate the theory.

ISSN:0090-9491    

DOI:10.1080/17442508308833282

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor