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Identification and quantification of irreversibility in stochastic systems.

Phys Chem Chem Phys
Ghosal A, Bisker G.
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Strong Markov Processes

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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Hidden Markov processes

IEEE Transactions on Information Theory, 2002
Summary: An overview of statistical and information-theoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel. In recent years, the work of \textit{L. E. Baum} and \textit{R.E. Petrie}, Ann. Math. Stat.
Yariv Ephraim, Neri Merhav
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MARKOV DECISION PROCESSES

Statistica Neerlandica, 1985
AbstractA review is presented of the development over the years of the theory and practical use of Markov decision processes. To this purpose three periods are considered: before 1966, from 1966 till 1972, and after 1973. In all 3 periods there has been some contribution from the Netherlands, but particularly in the last period the research in the ...
Wal, van der, J., Wessels, J.
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Markov Functionals of an Ergodic Markov Process

Theory of Probability & Its Applications, 1995
Let \((X(t), t \geq 0)\) 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, 1984
Translation from Teor. Veroyatn. Primen. 28, No.4, 653-667 (Russian) (1983; Zbl 0539.60088).
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Molecular Markov Processes

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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Piecewise Markov Processes

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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Symmetrizations of Markov processes

Journal of Theoretical Probability, 1988
The 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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