摘要:

A new class of iterative algorithms for solving undiscounted Bellman equations is proposed in this article, Such algorithms are proved to be particularly useful in handling “degenerate” equations. For simplicity of presentation and for motivation of basic ideas, the algorithms are introduced in terms of three control problems, one optimal stopping time problem and two singular stochastic control problems. The convergence and rates of convergence are obtained. These results are based on the introduction of a performance index of approximation, which makes new algorithms differ from the existing ones for solving regular undiscounted Bellman equations in the control literature.

ISSN:0163-0563    

DOI:10.1080/01630569008816367

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We characterize bestLpapproximation tofεLp[0,1] fromn-convex functions inLp[0,1], for 1≤p<∞ and for a positive integern. This characterization is used to derive some additional properties of the best approximations.

ISSN:0163-0563    

DOI:10.1080/01630569008816368

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We consider bifurcation points of the equationwhere, are linear mappings;Kis a nonlinear mapping of” higher order ”are functionswithman even number; and μ is a real number . Given a characteristic value of the pair (T, L0) such that the mappingT−L0() is a Fredholm operator with nullitypand index zero, we prove, under additional hypotheses, that (, 0) is a bifurcation point; moreover, in general ( in some special cases ), there exist at least 2 ( 2p, respectively ) distinct parameter families of nontrivial solutions in a neighborhood of (,0)

ISSN:0163-0563    

DOI:10.1080/01630569008816369

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630569008816356

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor