Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

Controlled semi-Markov fields with graph-structured compact state space


Authors: H. Daduna, P. S. Knopov and R. K. Chorney
Translated by: The authors
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal: Theor. Probability and Math. Statist. 69 (2004), 39-53
MSC (2000): Primary 60K15, 60K35, 90C40
Published electronically: February 7, 2005
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce locally acting distributed decision makers in the theory of semi-Markov decisions for systems for which both the domain and the action space are general and compact. Such decision makers are characterized by making decisions on the basis of the information gathered at their local neighborhood only. The state transient function of the system also is of a local structure. We consider general holding times of the systems and this results in semi-Markov properties in time. The neighborhood structure of the systems resembles in space the Markov property of spatial processes. Under some regularity assumptions, we reduce the optimal problems within the set of local strategies to the corresponding problems for deterministic Markov strategies.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60K15, 60K35, 90C40

Retrieve articles in all journals with MSC (2000): 60K15, 60K35, 90C40


Additional Information

H. Daduna
Affiliation: Universität Hamburg, Fakultät Mathematik, Bundesstrasse 55, D–20146 Hamburg, Germany
Email: amos801@math.uni-Hamburg.de

P. S. Knopov
Affiliation: Glushkov Institute for Cybernetics, National Academy of Sciences of Ukraine, Academician Glushkov Avenue 40, Kiev–187, 03680, Ukraine
Email: knopov1@yahoo.com

R. K. Chorney
Affiliation: Inter-Regional Academy of Personnel Management, Department of Mathematics, Frometivs’ka Street 2, Kiev–39, 03039, Ukraine

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00612-5
PII: S 0094-9000(05)00612-5
Keywords: Semi-Markov processes, Markov renewal processes, optimal control, average asymptotic reward, renewal reward processes, random fields, local strategies
Received by editor(s): January 24, 2003
Published electronically: February 7, 2005
Additional Notes: The research of the second author was partially supported by a grant from Deutsche Forschungsgemeinschaft at Hamburg University
Article copyright: © Copyright 2005 American Mathematical Society