The Theory of Stochastic Processes II by Gikhman, I.I.; Skorokhod, A.V.;

Short description:

From the Reviews:

"Gihman and Skorohod have done an excellent job of presenting the theory in its present state of richt imperfection."
D.W. Stroock in Bulletin of the American Mathematical Society, 1980

"To call this work encyclopedic would not give an accurate picture of its contant and style. Some parts read like a textbook, but others are more technical and contain relatively new results. ... The exposition is robust and explicit, as one has come to expect of the Russian tradition of mathematical writing. The set when completed will be an invaluable source of information and reference in this ever-expanding field"
K.L. Chung in American Scientist, 1977

"..., the subject has grown enormously since 1953, and there will never be a true successor to Doob's book, but Gihman and Skorohod's three volumes will, I think, occupy a rather similar position as an invaluable tool of reference for all probability theorists. ... The dominant impression is of the authors' mastery of their material, and of their confident insight into its underlying structure. ..."
J.F.C. Kingman in Bulletin of the London Mathematical Society, 1977

Long description:

From the Reviews: "To call this work encyclopedic would not give an accurate picture of its content and style. Some parts read like a textbook, but others are more technical and contain relatively new results. ... The exposition is robust and explicit, as one has come to expect of the Russian tradition of mathematical writing." --K.L. Chung, American Scientist, 1977

From the Reviews:

"Gihman and Skorohod have done an excellent job of presenting the theory in its present state of rich imperfection."
D.W. Stroock in Bulletin of the American Mathematical Society, 1980

"To call this work encyclopedic would not give an accurate picture of its content and style. Some parts read like a textbook, but others are more technical and contain relatively new results. ... The exposition is robust and explicit, as one has come to expect of the Russian tradition of mathematical writing. The set when completed will be an invaluable source of information and reference in this ever-expanding field"
K.L. Chung in American Scientist, 1977

"The dominant impression is of the authors' mastery of their material, and of their confident insight into its underlying structure. ..."
J.F.C. Kingman in Bulletin of the London Mathematical Society, 1977

Table of Contents:

I. Basic Definitions and Properties of Markov Processes.-
1. Wide-Sense Markov Processes.-
2. Markov Random Functions.-
3. Markov Processes.-
4. Strong Markov Process.-
5. Multiplicative Functional.-
6. Properties of Sample Functions of Markov Processes.- II. Homogeneous Markov Processes.-
1. Basic Definitions.-
2. The Resolvent and the Generating Operator of a Weakly Measurable Markov Process.-
3. Stochastically Continuous Processes.-
4. Feller Processes in Locally Compact Spaces.-
5. Strong Markov Processes in Locally Compact Spaces.-
6. Multiplicative Additive Functionals, Excessive Functions.- III. Jump Processes.-
1. General Definitions and Properties of Jump Processes.-
2. Homogeneous Markov Processes with a Countable Set of States.-
3. Semi-Markov Processes.-
4. Markov Processes with a Discrete Component.- IV. Processes with Independent Increments.-
1. Definitions. General Properties.-
2. Homogeneous Processes with Independent Movements. One-Dimensional Case.-
3. Properties of Sample Functions of Homogeneous Processes with Independent Increments in ?1.-
4. Finite-Dimensional Homogeneous Processes with Independent Increments.- V. Branching Processes.-
1. Branching Processes with Finite Number of Particles.-
2. Branching Processes with a Continuum of States.-
3. General Markov Processes with Branching.- Historical and Bibliographical Remarks.