A. N. Kolmogorov - the founder of the theory of reversible Markov processes

CONTENTS § 1. Introduction § 2. Reversible processes § 3. Reversible locally discrete Markov processes with interaction § 4. Reversible diffusion processes with interaction § 5. The invariance principle for reversible processes § 6. The concept of reversibility in the theory of queues References

[1]  Hans Föllmer,et al.  An entropy approach to the time reversal of diffusion processes , 1985 .

[2]  Donald F. Towsley,et al.  Product Form and Local Balance in Queueing Networks , 1977, JACM.

[3]  Benjamin Melamed,et al.  On the reversibility of queueing networks , 1982 .

[4]  U. Haussmann.  On the drift of a reversed diffusion , 1985 .

[5]  U. Haussmann,et al.  Time reversal of diffusion processes , 1985 .

[6]  E. Reich.  Note on Queues in Tandem , 1963 .

[7]  F. Spitzer.  Interaction of Markov processes , 1970 .

[8]  E. Pardoux,et al.  Time-reversal of diffusion processes and non-linear smoothing , 1985 .

[9]  R. R. P. Jackson,et al.  Queueing Systems with Phase Type Service , 1954 .

[10]  D. Stroock,et al.  Simulated annealing via Sobolev inequalities , 1988 .

[11]  R. Glauber.  Time‐Dependent Statistics of the Ising Model , 1963 .

[12]  P. Burke.  The Output of a Queuing System , 1956 .

[13]  R. Lang.  Unendlich-dimensionale Wienerprozesse mit Wechselwirkung , 1977 .

[14]  D. Stroock,et al.  Applications of the stochastic Ising model to the Gibbs states , 1976 .

[15]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Jean-Pierre Fouque,et al.  Hydrodynamical Limit for the Asymmetric Simple Exclusion Process , 1987 .

[17]  V. V. Anshelevich,et al.  Symmetric random walks in random environments , 1982 .

[18]  Frank Kelly,et al.  Reversibility and Stochastic Networks , 1979 .

[19]  A. N. Rybko,et al.  On Jackson Networks on Denumerable Graphs , 1989 .

[20]  Austin J. Lemoine.  ON SOJOURN TIME IN JACKSON NETWORKS OF QUEUES , 1987 .

[21]  C. Kipnis,et al.  DERIVATION OF THE HYDRODYNAMICAL EQUATION FOR THE ZERO-RANGE INTERACTION PROCESS , 1984 .

[22]  J. Fritz.  Stationary measures of stochastic gradient systems, infinite lattice models , 1982 .

[23]  P. Ferrari,et al.  An invariance principle for reversible Markov processes. Applications to random motions in random environments , 1989 .

[24]  H. Georgii.  Canonical Gibbs Measures , 1979 .

[25]  S. Varadhan,et al.  Ohrnstein—uhlenbeck process in a random potential , 1985 .

[26]  D. Stroock,et al.  Diffusions on an infinite dimensional torus , 1981 .

[27]  Brian D. O. Anderson,et al.  Reverse time diffusions , 1985 .

[28]  D. Stroock,et al.  L2 theory for the stochastic Ising model , 1976 .

[29]  B. Tóth.  Persistent random walks in random environment , 1986 .

[30]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[32]  H. Föllmer,et al.  Time reversal of infinite-dimensional diffusions , 1986 .

[33]  Frank Kelly,et al.  Networks of queues with customers of different types , 1975, Journal of Applied Probability.

[34]  K. Meyer.  The Output of a Queueing System , 1981 .

[35]  A. Kolmogoroff.  Zur Theorie der Markoffschen Ketten , 1936 .

[36]  R. Arratia.  The Motion of a Tagged Particle in the Simple Symmetric Exclusion System on $Z$ , 1983 .

[37]  A. Barbour.  Networks of queues and the method of stages , 1976, Advances in Applied Probability.

[38]  C. Kipnis.  Central Limit Theorems for Infinite Series of Queues and Applications to Simple Exclusion , 1986 .

[39]  Daniel W. Stroock,et al.  In one and two dimensions, every stationary measure for a stochastic Ising Model is a Gibbs state , 1977 .

[40]  On the stationary measures of anharmonic systems in the presence of a small thermal noise , 1986 .

[41]  E. Reich.  Waiting Times When Queues are in Tandem , 1957 .

[42]  David Ruelle,et al.  Observables at infinity and states with short range correlations in statistical mechanics , 1969 .

[43]  R. Dobrushin.  The problem of uniqueness of a gibbsian random field and the problem of phase transitions , 1968 .

[44]  A. Shimizu,et al.  Infinite dimensional stochastic differential equations and their applications , 1980 .

[45]  F. Kelly,et al.  Networks of queues , 1976, Advances in Applied Probability.

[46]  B. Gidas.  Nonstationary Markov chains and convergence of the annealing algorithm , 1985 .

[47]  David A. Castañón,et al.  Reverse-time diffusion processes , 1982, IEEE Trans. Inf. Theory.

[48]  E. Andjel.  Invariant Measures for the Zero Range Process , 1982 .

[49]  B. Melamed.  Characterizations of Poisson traffic streams in Jackson queueing networks , 1979, Advances in Applied Probability.

[50]  R. Holley.  Pressure and Helmholtz free energy in a dynamic model of a lattice gas , 1972 .

[51]  D. Kendall.  Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain , 1953 .

[52]  G. Royer.  Processus de diffusion associe a certains modeles d'Ising a spins continus , 1979 .

[53]  M. Nagasawa.  Time Reversions of Markov Processes , 1964, Nagoya Mathematical Journal.

[54]  A. Kolmogoroff,et al.  Zur Umkehrbarkeit der statistischen Naturgesetze , 1937 .

[55]  Infinite lattice systems of interacting diffusion processes, existence and regularity properties , 1982 .

[56]  P. Hohenberg,et al.  Theory of Dynamic Critical Phenomena , 1977 .

[57]  G. Fayolle,et al.  Sojourn Times in a Tandem Queue with Overtaking: Reduction to a Boundary Value Problem , 1986 .

[58]  S. Varadhan,et al.  Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions , 1986 .

[59]  B. Anderson.  Reverse-time diffusion equation models , 1982 .

[60]  L. Onsager.  Reciprocal Relations in Irreversible Processes. II. , 1931 .

[61]  R. Holley,et al.  Free energy in a Markovian model of a lattice spin system , 1971 .