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Zaharopol R. — Invariant Probabilities of Markov-Feller Operators and Their Supports
Zaharopol R. — Invariant Probabilities of Markov-Feller Operators and Their Supports

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Название: Invariant Probabilities of Markov-Feller Operators and Their Supports

Автор: Zaharopol R.

Аннотация:

In this book invariant probabilities for a large class of discrete-time homogeneous Markov processes known as Feller processes are discussed. These Feller processes appear in the study of iterated function systems with probabilities, convolution operators, certain time series, etc. Rather than dealing with the processes, the transition probabilities and the operators associated with these processes are studied.
Main features:
- an ergodic decomposition which is a "reference system" for dealing with ergodic measures
- "formulas" for the supports of invariant probability measures, some of which can be used to obtain algorithms for the graphical display of these supports
- helps to gain a better understanding of the structure of Markov-Feller operators, and, implicitly, of the discrete-time homogeneous Feller processes
- special efforts to attract newcomers to the theory of Markov processes in general, and to the topics covered in particular
- most of the results are new and deal with topics of intense research interest.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 108

Добавлена в каталог: 02.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C_0 (X)$-equicontinuous Markov — Feller pair (S, T) (or operator S)      76
$C_b(X)$-equicontinuous Markov — Feller pair (S, T) (or operator S)      76
$\Omega\Gamma$ decomposition      38
$\sigma$-compact topological space      6
(S, T)-ergodic measure      18
Abstract $L^1$-space      29
AL-space      29
Almost everywhere (a.e.) convergence      20
Alphabet      48
AM-space      29
AM-space, with unit      29
Archimedean Riesz space      31
Attractive probability      18
Banach lattice      29
Banach limit      25
Band      31
Band; generated by a subset of a Riesz space      31
Begins with (the word) w (about a sequence of letters of some alphabet)      49
Bounded sequence of real-valued functions      35
Characteristic function of a word      49
Common (absolute) maximum      67
Contraction      3 20 30
DGP condition      61
DGP-A condition      70
Dirac measure      3
Disjoint complement of a nonempty subset A of a Riesz space E      31
Dissipative Markov — Feller pair      22
Dissipative part of X (generated by a Markov — Feller pair)      22
Distance from a point $x \in X$ to a subset A of X      19
Dominant generic point      61
Dominant generic point for a subset A of X      70
e.m.d.s. property      80
Elementary measure      39
Equicontinuous family (or sequence) on the compact subsets of a metric space      33
Equicontinuous family of real-valued functions      32
Equicontinuous family of real-valued functions on a subset of a metric space      32
Equicontinuous sequence of real-valued functions      32
Equicontinuous sequence of real-valued functions, on a subset of a metric space      32
Ergodic measure      18
Feller operator      3
Foias operator      54
Generic point (for a Markov — Feller pair)      61
Ideal      30
Invariant (sub)set      14
Invariant probability      17
Invariant set (with respect to P)      18
Isometric and order isomorphic (about two Banach lattices)      30
Letter (of an alphabet)      48
Lexicographical order      29
Linear lattice      28
Lipschitz function      28
Logistic map      15
Markov operator      3 20 30
Markov operator, generated (or defined) by a transition probability      5
Markov pair (defined by a transition probability P)      43
Markov — Feller kernel      53
Markov — Feller operator      3
Markov — Feller pair      3
Markov — Feller pair, induced by a continuous function      13
Markov — Feller pair, induced by a kernel      54
Markov — Feller pair, induced by a probability $\mu_0$ and a kernel k      54
Markov — Feller pair, induced by a transition probability (in general metric spaces (not necessarily locally compact, or separable)      43
Minimal Markov — Feller pair (or operator)      51
Minimal set (with respect to a continuous function)      15
Minimal symbolic flow      15
Monotone class of subsets of a set X      11
Nonsingular (generic) point      61
Orbit of an element $x\in X$ under the action of a Markov — Feller operator or pair      44
Orbit-closure of an element $x\in X$ under the action of a Markov — Feller operator or pair      44
Order ideal      30
Order isomorphic (about two Banach lattices)      30; see “Isometric and order isomorphic”
Order unit (strong)      29
Ordered vector space      28
P-invariant set      18
Positive element,      2 28
Positive element, in the topological dual E' of a Banach lattice E      30
Positive operator      3 20 30
Quadratic map      15
Quasi-regular point (for a Markov — Feller pair)      61
Regular word (for a sequence of letters of an alphabet)      49
Riesz space      28
Ring of subsets of a set X      11
Rotation of the unit circle      14
Second disjoint complement of a nonempty subset A of a Riesz space E      31
Singular (generic) point      61
Standard extension of a measure $\mu$      18
Starts with (the word) w (about a sequence of letters of some alphabet)      49
Strictly ergodic      18
Strong order unit      29
Strongly regular word (for a sequence of letters of an alphabet)      49
Support of a continuous function      9
Symbolic flow      15
T-ergodic measure      18
T-invariant measure      17
T-invariant probability      17
Tight sequence of probabilities      95
Tight set of probabilities      95
Topological limit of a sequence of subsets of a metric space      24
Topological lower limit of a sequence of subsets of a metric space      24
Topological support of a (continuous) function      9
Topological upper limit of a sequence of subsets of a metric space      24
Topologically connected Markov — Feller pair (or operator)      51
Topologically convergent sequence of subsets of a metric space      24
Transition probability      4
Trivially minimal Markov — Feller pair      53
Uniform convergence (of a sequence of real-valued functions) on the compact subsets of a metric space      34
Uniform limit (of a sequence of real-valued functions) on the compact subsets of a metric space      34
Uniformly $C_0(X)$-equicontinuous (Markov — Feller pair (S, T) or operator S)      76
Uniformly $C_0(X)$-equicontinuous (Markov — Feller pair (S, T) or operator S) on the compact subsets of X      76
Uniformly $C_b(X)$-equicontinuous (Markov — Feller pair (S, T) or operator S)      77
Uniformly Cauchy sequence of real-valued functions on the compact subsets of a metric space      34
Uniformly equicontinuous family (or sequence) on the compact subsets of a metric space      33
Uniformly equicontinuous family of real-valued functions      32
Uniformly equicontinuous family of real-valued functions on a subset of a metric space      32
Uniformly equicontinuous sequence of real-valued functions      32
Uniformly equicontinuous sequence of real-valued functions; on a subset of a metric space      32
Uniquely ergodic      18
Unit (strong order unit of an AM-space)      29
Universal element      60
Universal element with respect to a subset A of X      60
Vector lattice      28
Weak KBBY decomposition      38
Weak* mean ergodic      67
Weak* uniquely mean ergodic      96
Word (of length m with letters in A)      48
x leads to y, $x \in X$, $y \in X$      60
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