Lectures on random evolution /

Random evolution denotes a class of stochastic processes which evolve according to a rule which varies in time according to jumps. This is in contrast to diffusion processes, which assume that the rule changes continuously with time. Random evolutions provide a very flexible language, having the adv...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Pinsky, Mark A., 1940-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; River Edge, N.J. : World Scientific, Ã1991.
Temas:
Stochastic processes.
Semigroups.
Stochastic Processes
Processus stochastiques.
Semi-groupes.
MATHEMATICS > Probability & Statistics > General.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Ch. 0. Two-state random velocity model. 0.1. Two-state Markov chain
  • 0.2. Random velocity model
  • 0.3. Weak law and central limit theorem
  • 0.4. Distribution functions of two-state model
  • 0.5. Passage-time distributions
  • 0.6. Asymptotic behavior with probability one
  • ch. 1. Additive functionals of finite Markov chains. 1.1. Finite Markov chains
  • 1.2. Asymptotic properties of the transition matrix
  • 1.3. The weak law of large numbers and the central limit theorem
  • 1.4. Recurrence properties
  • 1.5. Limit theorems for discontinuous additive functionals
  • 1.6. Proof of the Markov property
  • ch. 2. General random evolutions. 2.1. Preliminaries on semigroups of operators
  • 2.2. Construction of random evolution process
  • 2.3. Discontinuous random evolutions
  • 2.4. Limit theorems for random evolutions
  • 2.5. Application to diffusion approximations
  • 2.6. Martingale formulation of random evolution
  • ch. 3. Applications to the Kinetic theory of gases. 3.1. Physical background
  • 3.2. Stochastic solution of the linearized Boltzmann equation
  • 3.3. Asymptotic analysis of the linearized Boltzmann equation
  • ch. 4. Applications to isotropic transport on manifolds. 4.1. The Rayleigh problem of random flights
  • 4.2. Isotropic transport process on a manifold
  • 4.3. Applications to recurrence
  • 4.4. Isotropic transport process of a frame field on a manifold
  • ch. 5. Applications to stability of random oscillators. 5.1. Linear stochastic systems with multiplicative noise
  • 5.2. Simple harmonic oscillator with small noise
  • 5.3. Nilpotent linear systems with small noise.

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