摘要:

This paper systematically surveys the development of stochastic quasigradient (SQG) methods.These methods make it possible to solve optimization problems without calculating the precise valuesw of objectives and constraints (let alone of their derivatives). For deterministic nonlinear optimization problems, these methods can be regarded as methods of random search. For stochastic programming problems. SQG methods generalize the well-known stochastic approximation methods for unconstrained optimization of the expectation of a random function to problems involving general constraints.

ISSN:0090-9491    

DOI:10.1080/17442508308833246

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

In the present work we give a generalization, on the one hand, of the main result of [1] on the existence of weak solutions (in the sense of joint solution-measure) for equations with driving martingales and random measures the coefficients of which depend on the solution-processXat eachtεR+only throughXt–, and on the other hand, of the main results of [2] on the existence of weak solutions (in the strict sense) for equations the coefficients of which depend on the past ofXbut with driving semimartingales. Thus we prove existence of weak solutions (in the strict sense) for the equations with driving martingales and random measures coefficients of which depend in a predictable way on the processX. In the course of the proof the weak solution turns out as in [1] and [2] to be regular, that is satisfying the condition 7.4 or 7.5 of [2]

ISSN:0090-9491    

DOI:10.1080/17442508308833247

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508308833248

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

LetX(n)=(Xk), 1≦k≦nbe random process with discrete time defined by its transition probabilities which belong to some parametric family. It is assumed that the parameters of the transition probabilities before and/or after disorder as well as the disorder time, are unknown. For statistical purposes the processes of Radon-Nikodym derivatives of the measures generated by processes with disorder at the time s with respect to the measure generated by process without disorder where 1≦s≦nare often used. In the paper general sufficient conditions are given for weak convergence of these processes. Some examples are given to illustrate the application of the results obtained.

ISSN:0090-9491    

DOI:10.1080/17442508308833249

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

LetPbe the transition matrix of a recurrent irreducible Markov chain onZ. We define a new Markov chain, modified fromP, with transition matrix [Ptilde](x,y=(1-α(x))P(x,y)plus;α(x,ywhere α(x) belongs to [0,1] andQis a Markovian matrix. IfPis positive recurrent, [Ptilde] is still positive recurrent if:where d is a distance onZdefined frompandman invariant measure byP. IfPis only recurrent, [Ptilde] is still recurrent with the condition (ii) alone for chainsPbelonging to a special class. In this class we find positive recurrent chains, random walks, chains whose jumps are bounded above by an exponential law.

ISSN:0090-9491    

DOI:10.1080/17442508308833250

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

Systems are considered where the state evolves either as a diffusion process or as a finitestate Markov process, and the measurement process consists either of a nonlinear function of the state with additive white noise or as a counting process with intensity dependent on the state. Fixed interval smooting is considered, and the first main result obtained expresses a smoothing probability or a probability density symmetrically in terms of forward filtered, reverse-time filterd and unfiltered quantities; an associated result replaces the unfiltered and reverse-time filtered qauantities by a likelihood function. Then stochastic differential equationsare obtained for the evolution of the reverse-time filtered probability or probability density and the reverse-time likelihood function. Lastly, a partial differential equation is obtained linking smoothed and forward filterd probabilities or probability densities; in all instances considered, this equation is not driven by any measurement process. The different approaches are also linked to known techniques applicable in the linear-Gaussian case.

ISSN:0090-9491    

DOI:10.1080/17442508308833251

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/1744250008833245

出版商:Gordon and Breach Science Publishers S. A.    

年代:1983

数据来源: Taylor