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Theory of Probability & Its Applications, 1956
Let $\mathcal{E}$ be a metric space, and suppose that $\mathfrak{B}$ is the Borel field generated by the open sets of $\mathcal{E}$. A stochastic process is defined on $\mathcal{E}$ if a function $x(t,\omega )$$(0 \leqq t < \infty ,\omega \in \Omega )$ and a system of probability measures ${\bf P}_x (x \in \mathcal{E})$ are given such that all ${\bf P ...
Dynkin, E. B., Yushkevich, A. A.
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Let $\mathcal{E}$ be a metric space, and suppose that $\mathfrak{B}$ is the Borel field generated by the open sets of $\mathcal{E}$. A stochastic process is defined on $\mathcal{E}$ if a function $x(t,\omega )$$(0 \leqq t < \infty ,\omega \in \Omega )$ and a system of probability measures ${\bf P}_x (x \in \mathcal{E})$ are given such that all ${\bf P ...
Dynkin, E. B., Yushkevich, A. A.
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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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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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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, 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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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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In situ learning using intrinsic memristor variability via Markov chain Monte Carlo sampling
Nature Electronics, 2021Thomas Dalgaty +2 more
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