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  • Produktbild: Homogeneous Denumerable Markov Processes
  • Produktbild: Homogeneous Denumerable Markov Processes

Homogeneous Denumerable Markov Processes

Fr. 72.90

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

06.12.2011

Verlag

Springer Berlin

Seitenzahl

281

Maße (L/B/H)

24.4/17/1.7 cm

Gewicht

520 g

Auflage

Softcover reprint of the original 1st ed. 1988

Sprache

Englisch

ISBN

978-3-642-68129-5

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

06.12.2011

Verlag

Springer Berlin

Seitenzahl

281

Maße (L/B/H)

24.4/17/1.7 cm

Gewicht

520 g

Auflage

Softcover reprint of the original 1st ed. 1988

Sprache

Englisch

ISBN

978-3-642-68129-5

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: Homogeneous Denumerable Markov Processes
  • Produktbild: Homogeneous Denumerable Markov Processes
  • I Construction Theory of Sample Functions of Homogeneous Denumerable Markov Processes.- I The First Construction Theorem.-
    1.1 Introduction.-
    1.2 Definition of transformation gn.-
    1.3 Convergence of the sequence X(n)(?) (n?1).-
    1.4 Further properties of X(n)(?) (n?1).-
    1.5 The first construction theorem.- II The Second Construction Theorem.-
    2.1 Introduction.-
    2.2 The mapping Tmn.-
    2.3 The mapping Wn.-
    2.4 Constructing auxiliary functions.-
    2.5 The second construction theorem.-
    2.6 Summary.-
    2.7 Two notes.- II Theory of Minimal Nonnegative Solutions for Systems of Nonnegative Linear Equations.- III General Theory.-
    3.1 Introduction.-
    3.2 Definition of a system of nonnegative linear equations and definition, existence and uniqueness of its minimal nonnegative solution.-
    3.3 Comparison theorem and linear combination theorem.-
    3.4 Localization theorem.-
    3.5 Connecting property of the minimal nonnegative solution.-
    3.6 Limit theorem.-
    3.7 Matrix representation.-
    3.8 Dual theorem.- IV Calculation.-
    4.1 Some lemmas.-
    4.2 Reduction of the problems.-
    4.3 Ordinary systems of strictly nonhomogeneous equations with dimension n.- V Systems of 1-Bounded Equations.-
    5.1 Introduction.-
    5.2 First-type leading-outside systems of equations.-
    5.3 First-type consistent systems of equations.-
    5.4 Tailed random systems of strictly nonhomogeneous equations.-
    5.5 Regular systems of equations.-
    5.6 Pseudo-normal systems of equations.-
    5.7 Pseudo-normal systems of equations of finite dimension.-
    5.8 Second-type regular systems of equations.- III Homogeneous Denumerable Markov Chains.- VI General Theory.-
    6.1 Introduction.-
    6.2 Transition probabilities.-
    6.3 Distribution and moments of the first passage time.-
    6.4 Distribution and moments of the first passage time of a homogeneous finite Markov chain.-
    6.5 Distribution and moments of the times of passage.-
    6.6 Criteria for recurrence.-
    6.7 Distribution and moments of additive functionals.-
    6.8 Derived Markov chains and criteria for atomic almost closed sets.- VII Martin Exit Boundary Theory.-
    7.1 Introduction.-
    7.2 Decomposition for Markov chains.-
    7.3 Limit behaviour of excessive functions.-
    7.4 Green functions and Martin kernels.-
    7.5 h-chains.-
    7.6 Limit theorem for Martin kernels.-
    7.7 Martin boundaries.-
    7.8 Distribution of x?.-
    7.9 Martin expressions of excessive functions.-
    7.10 Exit space.-
    7.11 Uniqueness theorem.-
    7.12 Minimal excessive functions.-
    7.13 Terminal random variables.-
    7.14 Criteria for potentials and excessive functions, Riesz decomposition.-
    7.15 Criteria for minimal harmonic functions, minimal potentials and minimal excessive functions.-
    7.16 Atomic exit spaces and nonatomic exit spaces.-
    7.17 Blackwell decomposition of the state space.- VIII Martin Entrance Boundary Theory.-
    8.1 Introduction.-
    8.2 The first group of lemmas.-
    8.3 Properties of finite excessive measures.-
    8.4 The second group of lemmas.-
    8.5 Entrance boundary.-
    8.6 Entrance space and the expressions of excessive measures.- IV Homogeneous Denumerable Markov Processes.- IX Minimal Q-Processes.-
    9.1 Introduction.-
    9.2 Transition probabilities.-
    9.3 Distribution and moments of the first passage time.-
    9.4 Criterion for the positive recurrence.-
    9.5 Distribution and moments of integral-type functionals.-
    9.6 Distribution and moments of integral-type functionals on pseudo-translatable sets.-
    9.7 Extensions of the results in
    9.3.- X Q-Processes of Order One.-
    10.1 Introduction.-
    10.2 Transition probabilities.-
    10.3 Distribution and moments of the first passage time.- XI Arbitrary Q-Processes.-
    11.1 Strengthening of the first construction theorem.-
    11.2 Transition probability.-
    11.3 Decomposition theorems for excessive measures and excessive functions.- V Construction Theory of Homogeneous Denumerable Markov Processes.- XII Criteria for the Uniqueness of Q-Processes.-
    12.1 Introduction.-
    12.2 Lemmas.-
    12.3 Proof of the main theorem.-
    12.4 The case of diagonal type.-
    12.5 The bounded case.-
    12.6 The case when E is finite.-
    12.7 The case of a branch Q-matrix.-
    12.8 Another criterion and the finite and nonconservative case.-
    12.9 Independence of the two conditions in Theorem 12.1.1.-
    12.10 Probability interpretation of Condition (i) in Theorem 12.1.1.- XIII Construction of Q-Processes.-
    13.1 Construction theorem.-
    13.2 Specifications of all the Q-processes.-
    13.3 Expression of $$\left\{ {Q,\,{\Pi _{{{\left( {\partial X} \right)}_{e,}}\,x\,E}}} \right\}$$-processes.-
    13.4 Discussion.- XIV Qualitative Theory.-
    14.1 Introduction.-
    14.2 Statement of results.-
    14.3 Reduction of the construction problem of B-type Q-processes, Doob processes.-
    14.4 Reduction of the construction problem of B?F-type Q-processes.-
    14.5 Proofs of Theorems 14.2.1–14.2.3.-
    14.6 Proof and examples of applications of Theorem 14.2.4.-
    14.7 Proofs of Theorems 14.2.5–14.2.10.