摘要:

A topology of compact-open type is defined on the set of pairs consisting of drift and diffusion coefficients for which the Stroock-Varadhan martingale problem has at least one solution. A characterisation is given of subcollections of this set such that the restriction to these subcollections of the function taking each pair into the set of solutions of the corresponding martingale problem is upper semi-continuous. Only weak boundedness conditions are imposed on the coefficients, so that the solutions of the martingale problems under consideration may “escape to infinity” over finite intervals with positive probability. This result is used to obtain a continuous dependence theorem for stochastic differential equations of the Markov type.

ISSN:0090-9491    

DOI:10.1080/17442508608833372

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

A two-dimensional partially observable diffusion type process is considered. Under the assumption that the coefficients of the system of the equations satisfy the functional Lipschitz condition only with respect to one of the space variables, and that the linear growth condition on the infinity is also satisfied, the innovation process existence is proved for the so-called “observable” component of the process. As a lemma we obtain a non-traditional stochastic analogy of the well-known Gronwall-Bellman's lemma.

ISSN:0090-9491    

DOI:10.1080/17442508608833373

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

In this note a family of minimum contrast functions is introduced for estimating a real parameter appearing in a linear, stationary stochastic differential equation assuming values in a real and separable Hilbert space. It is proved that the corresponding minimum contrast estimate based on a noise free, direct, time continuous measurement of sample path is asymptotically consistent and has an asymptotic normal distribution.

ISSN:0090-9491    

DOI:10.1080/17442508608833374

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

Making use of martingale theory, stochastic regression theory, and certain properties of matrix polynomials in the unit shift operator, we study the problem concerning how much excitation should be introduced into the inputs in a multivariable ARMAX system for (i) consistent estimation of the system parameters by the method of extended least squares, and (ii) asymptotically efficient adaptive regulation of the system by using a perturbed version of the classical self-tuning regulator. In this connection, it is shown how the classical persistency-of-excitation-type conditions on regression vectors of past inputs, outputs and noise terms can be translated into corresponding conditions involving the inputs alone. Moreover, much weaker types of excitation conditions than persistent excitation are introduced and studied.

ISSN:0090-9491    

DOI:10.1080/17442508608833375

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

We consider a linear regression model in continuous time with predetermined stochastic regressors and a local martingale as noise process. The method of estimation of the regression parameters is inspired by the classical least-squares estimate in the discrete time setting. It is shown that under a certain condition limiting the growth of the maximal eigenvalue of the design matrix with respect to the minimal eigenvalue, this “quasi-least-squares” estimate converges with probability one to the true parameter values. The proof uses results from semimartingale theory, in particular the transformation formula and some stability properties of local martingales.

ISSN:0090-9491    

DOI:10.1080/17442508608833376

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

Non-uniform rates of convergence to normality are derived for standardized sums of random variables which form a martingale difference array, with the sum of conditional variances being a constant in each row. As a consequence, we obtain probabilities of moderate deviations, convergence of absolute moments and (nonuniform)Lpversions of the Berry-Esseen theorem.

ISSN:0090-9491    

DOI:10.1080/17442508608833377

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

Stochastic integration theory is developed by axiomatizing the concept of semi-martingale in terms of a continuity property of integrals of simple functions. Using this approach, stochastic integration for left-continuous integrands, the change of variables formula and properties of the quadratic variation process are established in an elementary way. Submartingale decomposition theorems are introduced at a late stage in order to extend the results to general predictable integrands.

ISSN:0090-9491    

DOI:10.1080/17442508608833378

出版商:Gordon and Breach Science Publishers, Inc    

年代:1986

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508608833371

出版商:Gordon and Breach Science Publishers    

年代:1986

数据来源: Taylor