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This volume is representative of the work of Chinese probabilitists on probability theory and its applications in physics. Many interesting results of Jump Markov Processes are discussed, and a very fashionable new class of Markov processes — Markov interacting processes with noncompact states, including the important Schlögl model taken from statistical physics, is also considered. The main body of this book is self-contained and can be used in a course on “Stochastic Processes” for graduate students.
Sample Chapter(s)
Starting From Markov Chains An Overview of the Book (738 KB)
Contents:
- Starting from Markov Chains. An Overview of the Book
- General Jump Processes:
- Transition Function and its Laplace Transform
- Existence and Simple Constructions of Jump Processes
- Uniqueness Criteria
- Recurrence, Ergodicity and Invariant Measures
- Probability Metrics and Coupling Methods
- Symmetrizable Jump Processes:
- Symmetriz-able Jump Processes and Dirichlet Forms
- Field Theory
- Large Deviations
- Spectral Gap
- Equilibrium Particle Systems:
- Random Fields
- Reversible Spin Processes and Exclusion Processes
- Yang-Mills Lattice Fields
- Non-Equilibrium Particle Systems:
- Constructions of the Processes
- Existence of the Stationery Distributions and Ergodicity
- Phase Transitions
- Hydrodynamic Limits
Readership: Mathematicians, researchers in probability, physicists and graduate students in related fields.
