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Markov Chain Models--Rarity and Exponentiality (Applied Mathematical Sciences 28) - J. Keilson
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ISBN: 0387904050

[SR: 5826179], Paperback, [EAN: 9780387904054], Springer, Springer, Book, [PU: Springer], Springer, in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over­ view of the material and ideas covered. The presentation is loose and fragmentary, and should be read lightly initially. Subsequent perusal from time to time may help tie the mat­ erial together and provide a unity less readily obtainable otherwise. The detailed presentation begins in Chapter 1, and some readers may prefer to begin there directly. §O.l. Time-Reversibility and Spectral Representation. Continuous time chains may be discussed in terms of discrete time chains by a uniformizing procedure (§2.l) that simplifies and unifies the theory and enables results for discrete and continuous time to be discussed simultaneously. Thus if N(t) is any finite Markov chain in continuous time governed by transition rates vmn one may write for pet) = [Pmn(t)] • P[N(t) = n I N(O) = m] pet) = exp [-vt(I - a )] (0.1.1) v where v > Max r v ' and mn m n law ~ 1 - v-I * Hence N(t) where is governed r vmn Nk = NK(t) n K(t) is a Poisson process of rate v indep- by a ' and v dent of N • k Time-reversibility (§1.3, §2.4, §2.S) is important for many reasons. A) The only broad class of tractable chains suitable for stochastic models is the time-reversible class, 5241, Gardening & Landscape Design, 10828041, By Climate, 5303, By Region, 5310, By Technique, 52072011, English Gardens, 5246, Essays, 5248, Flowers, 5269, Fruit, 5271, Garden Design, 5274, Garden Furnishings, 5278, Greenhouses, 5280, Herbs, 5283, House Plants, 5289, Japanese Gardens, 5291, Landscape, 5293, Lawns, 5297, Ornamental Plants, 5299, Outdoor & Recreational Areas, 5301, Reference, 5304, Shade, 5306, Shrubs, 572308, Soil, 5313, Trees, 5315, Vegetables, 52074011, Weed & Pest Control, 52075011, Wild Plants, 48, Crafts, Hobbies & Home, 1000, Subjects, 283155, Books, 13983, Probability & Statistics, 226699, Applied, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 491548, Statistics, 468218, Mathematics, 468216, Science & Mathematics, 465600, New, Used & Rental Textbooks, 2349030011, Specialty Boutique, 283155, Books

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Markov Chain Models--Rarity and Exponentiality (Applied Mathematical Sciences 28) - Taschenbuch

ISBN: 0387904050

[SR: 5826179], Paperback, [EAN: 9780387904054], Springer, Springer, Book, [PU: Springer], Springer, in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over­ view of the material and ideas covered. The presentation is loose and fragmentary, and should be read lightly initially. Subsequent perusal from time to time may help tie the mat­ erial together and provide a unity less readily obtainable otherwise. The detailed presentation begins in Chapter 1, and some readers may prefer to begin there directly. §O.l. Time-Reversibility and Spectral Representation. Continuous time chains may be discussed in terms of discrete time chains by a uniformizing procedure (§2.l) that simplifies and unifies the theory and enables results for discrete and continuous time to be discussed simultaneously. Thus if N(t) is any finite Markov chain in continuous time governed by transition rates vmn one may write for pet) = [Pmn(t)] • P[N(t) = n I N(O) = m] pet) = exp [-vt(I - a )] (0.1.1) v where v > Max r v ' and mn m n law ~ 1 - v-I * Hence N(t) where is governed r vmn Nk = NK(t) n K(t) is a Poisson process of rate v indep- by a ' and v dent of N • k Time-reversibility (§1.3, §2.4, §2.S) is important for many reasons. A) The only broad class of tractable chains suitable for stochastic models is the time-reversible class, 5241, Gardening & Landscape Design, 10828041, By Climate, 5303, By Region, 5310, By Technique, 52072011, English Gardens, 5246, Essays, 5248, Flowers, 5269, Fruit, 5271, Garden Design, 5274, Garden Furnishings, 5278, Greenhouses, 5280, Herbs, 5283, House Plants, 5289, Japanese Gardens, 5291, Landscape, 5293, Lawns, 5297, Ornamental Plants, 5299, Outdoor & Recreational Areas, 5301, Reference, 5304, Shade, 5306, Shrubs, 572308, Soil, 5313, Trees, 5315, Vegetables, 52074011, Weed & Pest Control, 52075011, Wild Plants, 48, Crafts, Hobbies & Home, 1000, Subjects, 283155, Books, 13983, Probability & Statistics, 226699, Applied, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 491548, Statistics, 468218, Mathematics, 468216, Science & Mathematics, 465600, New, Used & Rental Textbooks, 2349030011, Specialty Boutique, 283155, Books

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in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over view of the material and ideas covered. The presentation is loose and fragmentary, and should be read lightly initially. Subsequent perusal from time to time may help tie the mat erial together and provide a unity less readily obtainable otherwise. The detailed presentation begins in Chapter 1, and some readers may prefer to begin there directly., [PU: Springer]

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Markov Chain Models--Rarity and Exponentiality (Applied Mathematical Sciences 28) - J. Keilson
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1979, ISBN: 9780387904054

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Details zum Buch
Markov Chain Models - Rarity and Exponentiality (Applied Mathematical Sciences)
Autor:

Keilson, Julian; Keilson, J.

Titel:

Markov Chain Models - Rarity and Exponentiality (Applied Mathematical Sciences)

ISBN-Nummer:

in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over­ view of the material and ideas covered. The presentation is loose and fragmentary, and should be read lightly initially. Subsequent perusal from time to time may help tie the mat­ erial together and provide a unity less readily obtainable otherwise. The detailed presentation begins in Chapter 1, and some readers may prefer to begin there directly. §O.l. Time-Reversibility and Spectral Representation. Continuous time chains may be discussed in terms of discrete time chains by a uniformizing procedure (§2.l) that simplifies and unifies the theory and enables results for discrete and continuous time to be discussed simultaneously. Thus if N(t) is any finite Markov chain in continuous time governed by transition rates vmn one may write for pet) = [Pmn(t)] • P[N(t) = n I N(O) = m] pet) = exp [-vt(I - a )] (0.1.1) v where v > Max r v ' and mn m n law ~ 1 - v-I * Hence N(t) where is governed r vmn Nk = NK(t) n K(t) is a Poisson process of rate v indep- by a ' and v dent of N • k Time-reversibility (§1.3, §2.4, §2.S) is important for many reasons. A) The only broad class of tractable chains suitable for stochastic models is the time-reversible class

Detailangaben zum Buch - Markov Chain Models - Rarity and Exponentiality (Applied Mathematical Sciences)


EAN (ISBN-13): 9780387904054
ISBN (ISBN-10): 0387904050
Taschenbuch
Erscheinungsjahr: 1979
Herausgeber: SPRINGER VERLAG GMBH
208 Seiten
Gewicht: 0,318 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 29.02.2008 08:19:39
Buch zuletzt gefunden am 25.04.2017 23:39:34
ISBN/EAN: 0387904050

ISBN - alternative Schreibweisen:
0-387-90405-0, 978-0-387-90405-4


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