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Markov Functionals of an Ergodic Markov Process
Theory of Probability & Its Applications, 1995Let \((X(t), t \geq 0)\) be a homogeneous Markov process. The author calls a random process \(\xi(t)\) the Markovian functional if the pair \((X(t), \xi(t))\) is a homogeneous Markov process. Let \(\xi_n (t)\) be a sequence of Markovian functionals with finite state space \(I = \{1,2,\dots, d\}\) for all \(n \geq 1\) and such that the following ...
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Representation of a Semi-Markov Process as a Time-Change Markov Process
Theory of Probability & Its Applications, 1984Translation from Teor. Veroyatn. Primen. 28, No.4, 653-667 (Russian) (1983; Zbl 0539.60088).
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Nature, 1970
Markov processes are encountered in many contexts in physics and chemistry. This review surveys the scope of their application.
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Markov processes are encountered in many contexts in physics and chemistry. This review surveys the scope of their application.
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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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Symmetrizations of Markov processes
Journal of Theoretical Probability, 1988The authors discuss two methods of symmetrizing Markov processes. The first method applies to some Lévy processes X on a compact Abelian group G, with \(\alpha\)-potential density \(u^{\alpha}(x,y)\). A condition is given which guarantees that \(v^{\alpha}(x,y)=u^{\alpha}(x,y)+u^{\alpha}(y,x)\) will be the \(\alpha\)-potential density of a symmetric ...
Glover, Joseph, Rao, Murali
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Theory of Probability & Its Applications, 1960
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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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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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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