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Advances in Applied Probability, 1980
Interacting Markov processes are obtained by superimposing some type of interaction on many otherwise independent Markovian subsystems. As a result of the interaction, the subsystems fail to have the Markov property; the system as a whole remains Markovian, however. This subject has grown rapidly during the past decade.
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Interacting Markov processes are obtained by superimposing some type of interaction on many otherwise independent Markovian subsystems. As a result of the interaction, the subsystems fail to have the Markov property; the system as a whole remains Markovian, however. This subject has grown rapidly during the past decade.
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On Conditional Markov Processes
Theory of Probability & Its Applications, 1960In this paper a pair of random processes $X_t $, $Y_t $, which conjunctly form the Markov process $Z_t $ is considered. The conditional distribution of the process $Y_t $ for the condition of a known realization of the process $X_t $ during some time interval is examined. E. B.
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Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1966
This chapter is concerned with many-to-one functions of Markov processes. Neither the Markov property nor the Chapman-Kolmogorov equation are generally satisfied by the derived processes determined by such functions. The first section considers special circumstances under which the Chapman-Kolmogorov equation is still satisfied by the derived process ...
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This chapter is concerned with many-to-one functions of Markov processes. Neither the Markov property nor the Chapman-Kolmogorov equation are generally satisfied by the derived processes determined by such functions. The first section considers special circumstances under which the Chapman-Kolmogorov equation is still satisfied by the derived process ...
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Markov and Semi-Markov Processes
2018This chapter is devoted to jump Markov processes and finite semi-Markov processes. In both cases, the index is considered as the calender time, continuously counted over the positive real line. Markov processes are continuous-time processes that share the Markov property with the discrete-time Markov chains.
Valérie Girardin, Nikolaos Limnios
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Russian Mathematical Surveys, 1973
This article is concerned with the foundations of the theory of Markov processes. We introduce the concepts of a regular Markov process and the class of such processes. We show that regular processes possess a number of good properties (strong Markov character, continuity on the right of excessive functions along almost all trajectories, and so on).
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This article is concerned with the foundations of the theory of Markov processes. We introduce the concepts of a regular Markov process and the class of such processes. We show that regular processes possess a number of good properties (strong Markov character, continuity on the right of excessive functions along almost all trajectories, and so on).
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Markov Processes and Markov Families
2012In this section we shall use intuitive arguments in order to find the distribution of M T . Rigorous arguments will be provided later in this chapter, after we introduce the notion of a strong Markov family. Thus, the problem at hand may serve as a simple example motivating the study of the strong Markov property.
Leonid Koralov, Yakov G. Sinai
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On Extensions of a Markov Process
Theory of Probability & Its Applications, 1968openaire +3 more sources
Stem Cell Differentiation as a Non-Markov Stochastic Process
Cell Systems, 2017Colin Please +2 more
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