摘要:

A 4–dimensional nonlinear system of ordinary differential equations was recently constructed by Antonelli and Seymour to model the European rabbit viral disease known as myxomatosis. This model is based on the documented Rothschild's effect, that is, on the hormonal control of flea reproduction by the rabbit. Our model incorporates density dependent rabbit reproductivity and total caloric intake over time. Three nonlinear filtering problems are considered here in which the signal process is always the entire 4–dimensional system but where the observations processes are, least squares estimation of the number or density of rabbits, estimation of flea numbers, and simultaneous estimation of rabbit densities and total caloric intake, respectively. Extensive use is made of H. Kunita's backward Stratonovich calculus and stochastic partial differential equations theory to obtain exact solution measures of the Zakai equation for these three problems

ISSN:0736-2994    

DOI:10.1080/07362998708809116

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

This paper deals with discrete–time approximation of nonlinear filtering problems in which both the state and observation processes are described by stochastic delay equations. The approach consists in approximating the original problem by Euler–type discrete–time model for which an optimal filter can be obtained by an explicit recursive procedure. The validity of the approach is substantiated by verifying the weak convergence of the approximating model to our original problem

ISSN:0736-2994    

DOI:10.1080/07362998708809117

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

Applications of the original prophet inequalities of Krengel and Sucheston are made to problems of order selection, non–measurable stop rules, look–ahead stop rules, and iterated maps of random variables. Also, proofs are given of two results of Hill and Hordijk concerning optimal orderings of uniform and exponential distributions

ISSN:0736-2994    

DOI:10.1080/07362998708809118

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

We prove the law of the iterated logarithm for solutions of Stochastic Differential Equations (SDEs) driven by continuous semiraartingales, under suitable conditions. This extends a result of Kulinich for classical diffusions to solutions of SDEs which are not necessarily Markov

ISSN:0736-2994    

DOI:10.1080/07362998708809119

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

A necessary and sufficient condition is given for the strong law of large numbers to hold for sequences of exchangeable random variables. This result is contrasted with the traditional results for independent random variables where moment conditions are generally sufficient. In addition, laws of large numbers are given for symmetrically, exchangeable random variables, and a characterization of symmetric exchangeability is given

ISSN:0736-2994    

DOI:10.1080/07362998708809120

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

The aim of the present study is to examine the sensitivity behavior of the Mantel χ2extension test based on ridit scores, which is widely used in biological cases, especially epidemio1ogical studies, to small incidence rates. Two additional statistical test, the conventional χ2contingency table analysis and the Solomon–Kullback information χ2test are also being studied

ISSN:0736-2994    

DOI:10.1080/07362998708809121

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

Methods of nonparametric inference are proposed for an irreversiblek-compartmental system. It is assumed that the time of transitions between the transient states is unobservable. Explicit expression for the estimator of the transition rate is provided. Asymptotic result is given. A comparsion is made with the maximum likelihood estimator which relies on observing the process continuously.

ISSN:0736-2994    

DOI:10.1080/07362998708809122

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

ISSN:0736-2994    

DOI:10.1080/07362998708809115

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor