No Access

ON CONTACT PROCESSES IN CONTINUUM

YURI KONDRATIEV

Department of Mathematics and BiBoS, Bielefeld University, Postfach 100131, D-33501 Bielefeld, Germany

National University "Kiev Mohyla Academy", Ukraine

Search for more papers by this author

and

ANATOLI SKOROKHOD

Department of Statistics and Probability, Michigan State University, E. Lansing, MI 48824, USA

Institute of Mathematics of NASU, Kiev, Ukraine

Search for more papers by this author

https://doi.org/10.1142/S0219025706002305Cited by:39 (Source: Crossref)

Abstract

We introduce a continuous version of the contact model which is well known and widely studied in the lattice case. Under certain general assumptions on the infection spreading characteristics, we construct the contact process as a Markov process in the configuration space of the system.

Keywords:

AMSC: 60K35, 60J75, 60J80, 82C21, 82C22

References

I. I. Gikhman and A. V. Skorokhod , The Theory of Stochastic Processes 2 ( Springer-Verlag , 1979 ) . Crossref, Google Scholar
R. A. Holley and D. W. Stroock, Acta Math. 140, 103 (1978), DOI: 10.1007/BF02392306. Crossref, Web of Science, Google Scholar
Yu. Kondratiev and O. Kutovyi, On topological properties of configuration spaces, BiBoS preprint, to appear in Math. Nachr. 2003 . Google Scholar
Yu. Kondratiev and E. Lytvynov, Ann. Inst. H. Poincaré, Ser. B 41, 685 (2005), DOI: 10.1016/j.anihpb.2004.05.002. Crossref, Web of Science, Google Scholar
Yu. Kondratiev and A. Skorokhod, Birth-and-death Markov processes in configuration spaces, in preparation, 2005 . Google Scholar
T. M. Liggett , Interacting Particle Systems ( Springer-Verlag , 1985 ) . Crossref, Google Scholar
T. M. Liggett , Stochastic Interacting Systems: Contact, Voter and Exclusion Processes ( Springer-Verlag , 1999 ) . Crossref, Google Scholar
C. Preston, Bull. Inst. Internat. Statist. 46, 371 (1975). Google Scholar