Dynkin E.B., Kovary T., Brown D.E. — Theory of Markov processes :: Электронная библиотека попечительского совета мехмата МГУ

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Dynkin E.B., Kovary T., Brown D.E. — Theory of Markov processes

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Название: Theory of Markov processes

Авторы: Dynkin E.B., Kovary T., Brown D.E.

Аннотация:

An investigation of the logical foundations of the theory behind Markov random processes, this text explores subprocesses, transition functions, and conditions for boundedness and continuity. Rather than focusing on probability measures individually, the work explores connections between functions. An elementary grasp of the theory of Markov processes is assumed.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 217

Добавлена в каталог: 15.12.2013

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Предметный указатель

$\lambda$ -System      1
$\mathscr{F}$ -bounded function      145
$\mathscr{F}$ -bounded process      145
$\pi$ -system      1
$\sigma$ -algebra      1
$\sigma$ -algebra generated by system $\mathcal{C}$       1
$\sigma$ -bicompact space      18
$\sigma$ -compact space      18
$\varepsilon$ -neighbourhood      18
Admissible set      6 9 94
Admissible system of sets      73
Almost certain equality      10
Analytic sets      176
Base of topological space      174
Bicompact      17
Bicompact space      17
Borel sets      19
Boundary of set      70
Canonical form of process      46
Canonical process      45 52
Canonical sequence of subdivisions      21
Canonical subprocess      57 89
Capacity      178
Characteristic function      4
Characteristic function of set      4
Closed set      17
Closure of set      17
Compact      174
Compact set      18
Compact space      17
Complete metric space      18
Complete transition function      96
Conditional expectation      11
Conditional probability      11
Continuous mapping      19
Continuous process      53
Convergence      17
Determinate motion with velocity $\upsilon$       97 170
Discontinuity of second kind      149
Discrete Markov process      17
Elementary events      10
Equivalent multiplicative functionals      90
Equivalent processes      46 50 51
Equivalent systems of sets      74
Equivalent systems, {}      59
Events      10
Everywhere dense set      17
Expectation      10
Feller process      136
Feller transition function      136
Hausdorff space      17
Inaccessible set      49
Instant of cut-off      26
Instant of first contact with set      188
Instant of first departure after $\eta$ of trajectory from system of sets      74
Instant of first departure after s of trajectory from interior of set      77 168
Instant of first departure after s of trajectory from set      69 187
Instant of first departure after s of trajectory from system of sets      73
Instant of first reaching set      187
Instant of jump      159
Jump-type process      159
Kolmogorov — Chepman equation      32
L-canonical process      47
L-system      4
Law of zero or unity      139
Lebesque integral      8
Locally bicompact space      18
Locally compact space      18
Markov chain      27

Markov family of random functions      28
Markov process      25
Markov process in time set $\Gamma$       27
Markov random function      27
Measurable function      3
Measurable mapping      3
Measurable process      105 123
Measurable space      3
Measure      7
Metric measurable space      21
Metric space      18
Multiplicative functional      61 90
Multiplicative functional of integral type      81
Narrowing of basic $\sigma$ -algebras      44
Neighbourhood      17
Non cut-off processes      26
Normal process      142
Normal system      74
Normal transition function      96
Open set      17 18
Part of process      70 94
Part of process corresponding to system $\mathscr{F}$       79
Phase space      26
Poisson process      160
Poisson transition function      99
probability      10
Probability measure      7
Probability process      197
Probability space      10
Process continuous from the right      53
Process continuous from the right at point x      137
Process continuous from the right up to instant $\eta$       149
Process continuous up to deparfrom $\Gamma$       149
Process continuous up to instant $\eta$       149
Process having no discontinuities of second kind      149
Process having no discontinuities of second kind up to departure from $\Gamma$       149
Process having no discontinuities of second kind up to instant $\eta$       149
Process of Feller's type at point x      137
Process quasi-stationary from left      169
Purging space of elementary events      44
Random variable      10
Random variable independent of future      123
Random variable independent of future and s-past      124
Semi-compact      174
Separable space      17
Shortening of life      53
Space of elementary events      26
Splitting of elementary events      44
Stationary process      35 41
Stationary transition function      101
Step process      159
Strictly Markov process      102 108
Subordinate process      44
Subordinate system of sets      74
Subprocess      53 54 88
Subprocess corresponding to admissible subset      68 94
Subprocess corresponding to multiplicative functional      61 90
Summable function      7
Topological measurable space      19
Topological product of spaces      18
Topological space      16
Trajectory      26
Transformation of space of elementary events      42
Transition function      26 36
Wiener process      171
Wiener process with break at point 0      171
Wiener process with reflection at point 0      171
Wiener transition function      98
’Rectangles’      18

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