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Author: Marius Iosifescu; Petre Tǎutu
Publisher: Bucureşti : Ed. Academiei [u.a.], 1973.
Series: Biomathematics, 3
Edition/Format:   Print book : English : Rev. and enl. vers
Vol. 1.

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Document Type: Book
All Authors / Contributors: Marius Iosifescu; Petre Tǎutu
ISBN: 038706270X 9780387062709 354006270X 9783540062707
OCLC Number: 60436150
Notes: Literaturverz. S. [303] - 320.
Description: 331 S : graph. Darst.
Contents: 1 Discrete parameter stochastic processes.- 1.1. Denumerable Markov chains.- 1.1.1. Preliminaries.- Definition of a Markov chain.- The existence theorem.- The n-step transition probabilities.- Strong Markov property.- 1.1.2. Classification of states.- Return states and recurrent states.- Regenerative phenomena.- Positive states and limit theorems.- Geometric ergodicity.- Essential states and classes of states.- Conditional motion.- 1.1.3. Taboo and stationarity.- Taboo transition probabilities.- Ratio limit theorems.- Stationary distributions.- Stationary measures.- Integral representations.- 1.1.4. Finite state Markov chains.- Specific properties.- The matrix method.- The Ehrenfest model.- 1.2. Noteworthy classes of denumerable Markov chains.- 1.2.1. Random walk.- Homogeneous random walk.- Some important special cases.- Barriers.- Generalizations.- Integral representations for certain nonhomogeneous random walks.- 1.2.2. Galton-Watson chains.- Basic properties.- Extinction probability.- Time to extinction.- Stationary distributions and stationary measures.- Spectral theory of Galton-Watson chains.- Asymptotic properties.- Multitype Galton-Watson chains.- 1.2.3. Markov chains occurring in queueing theory.- Preliminaries.- Queueing systems.- An imbedded Markov chain in the M/G/1 queue.- An imbedded Markov chain in the GI/M/1 queue.- 1.3. Markov chains with arbitrary state space.- 1.3.1. Preliminaries.- Definition and existence theorem.- Generalized n-step transition functions.- 1.3.2. Uniform ergodicity.- Uniform strong ergodicity.- Uniform weak ergodicity.- 1.3.3. The coefficient of ergodicity.- Definition and properties.- Application to uniform ergodicity.- Some limit theorems.- 1.3.4. Compact Markov chains.- Definition and properties.- Random systems with complete connections.- References.- 2 Continuous parameter stochastic processes.- 2.1. Some general problems.- 2.1.1. Preliminaries.- Definition of a stochastic process.- Finite dimensional distributions.- 2.1.2. Basic concepts.- Separability.- Stochastic continuity and measurability.- 2.1.3. Trajectories.- Generalities.- Continuous trajectories.- Trajectories without discontinuities of the second kind.- 2.1.4. Convergence of stochastic processes.- Weak convergence of processes.- The Prohorov theorem.- 2.2. Processes with independent increments.- 2.2.1. Preliminaries.- Definition and existence theorem.- Stochastic continuity.- 2.2.2. Basic processes with independent increments.- The Poisson process.- The Wiener process.- Brownian motion.- 2.2.3. General properties.- Integral decomposition.- The three parts decomposition.- 2.3. Markov processes.- 2.3.1. Preliminaries.- Transition functions.- Definition and existence theorem.- The strong Markov property.- The semi-group approach to homogeneous Markov processes.- 2.3.2. Markov jump processes. I. General theory.- Transition intensity functions.- The Kolmogorov-Feller equations.- Determining a transition function from its intensity.- The minimal process.- 2.3.3. Markov jump processes. II. Discrete state space.- The case of a finite state space.- The case of a denumerable state space.- Poisson processes as Markov jump processes.- Markov branching processes.- 2.3.4. Homogeneous Markov jump processes with discrete state space.- Preliminaries.- Continuity and differentiability properties.- The Kolmogorov differential equations.- Continuous parameter regenerative phenomena.- Properties of trajectories.- Discrete skeletons and classification of states.- Birth-and-death processes.- 2.3.5. Markov diffusion processes.- Classical diffusion processes.- The Kolmogorov equations.- Approximations.- Boundaries.- Brownian motion as diffusion process.- 2.3.6. Extensions of Markov processes.- Semi-Markov processes.- Renewal processes.- References.- Notation index.- Author index.
Series Title: Biomathematics, 3
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Vol. 1.


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