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SIAM Journal on Applied Mathematics, 1973
A piecewise Markov process is a discrete-state, continuous-parameter stochastic process which is Markovian within contiguous time-segments. Starting at the beginning of a segment in some initial state, the process evolves in a Markovian manner until the segment terminates at a random time whose distribution is completely determined by the initial state.
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A piecewise Markov process is a discrete-state, continuous-parameter stochastic process which is Markovian within contiguous time-segments. Starting at the beginning of a segment in some initial state, the process evolves in a Markovian manner until the segment terminates at a random time whose distribution is completely determined by the initial state.
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Bicategories of Markov Processes
2017We construct bicategories of Markov processes where the objects are input and output sets, the morphisms (one-cells) are Markov processes and the two-cells are simulations. This builds on the work of Baez, Fong and Pollard, who showed that a certain kind of finite-space continuous-time Markov chain (CTMC) can be viewed as morphisms in a category.
Florence Clerc +2 more
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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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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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Theory of Probability & Its Applications, 1957
The problem of constructing a strong Markov process with a given measurable Markov transition function $p(s,x,t,\Gamma )$ is considered. The space X of possible states is supposed to be given together with the function $p(s,x,t,\Gamma )$.If it is required that the sample functions $x(t,\omega )$ be defined for each $\omega $ at all $t \in [0,\infty )$,
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The problem of constructing a strong Markov process with a given measurable Markov transition function $p(s,x,t,\Gamma )$ is considered. The space X of possible states is supposed to be given together with the function $p(s,x,t,\Gamma )$.If it is required that the sample functions $x(t,\omega )$ be defined for each $\omega $ at all $t \in [0,\infty )$,
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Theory of Probability & Its Applications, 1960
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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 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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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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