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Fukushima M. — Dirichlet forms and markov process
Fukushima M. — Dirichlet forms and markov process

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Название: Dirichlet forms and markov process

Автор: Fukushima M.

Аннотация:

This book is an attempt to unify these two theories. By unification the theory of Markov process bears an intrinsic analytical tool of great use, while the theory of Dirichlet spaces acquires a deep probabilistic structure.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 196

Добавлена в каталог: 14.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absorbing barrier Brownian motion      112
Additive functional      124
Additive functional (of bounded variation)      143
Admissible family (of increasing u-fields)      88
Admissible system (of measures)      184
Approximating form      21
Beurling — Deny first formula      48 119
Beurling — Deny second formula      51 162
BLD function      68
Blumenthal 0-1 law      93
Boundary condition      59
Brownian motion      95
Capacity      62
Chaquet capacity      63
Closed form      4
Convolution semigroup on $\mathbb R^n$      29
Convolution semigroup on the unit circle      31
Core      5
Cosable form      4
Diffusion      94 113
Diffusion form      119
Diffusion part (of Dirichlet form)      51
Dirichlet form      5
Dirichlet form in the wide sense      27
Dirichlet integral      10
Dirichlet space      32
Doob’s inequality      126
Douglas integral      11
Dynkin formula      97
Energy (of additive functional)      134
Energy measure (of function)      152
Energy measure (of martingale additive functional)      135
Equilibrium potential      62 75
Equivalence (of additive functional)      124
Equivalence (of symmetric Hunt processes)      107
Exceptional set      96
Excessive function (with respect to $L^2$-semigroup)      69
Excessive function (with respect to transition function)      99
Extended Dirichlet space      35
Feller property      94
Finely continuous (open set)      93
Finely continuous q.e.      98
Friedrichs extension      53
Gauss’s quadratic form      76
Generator (of resolvent)      15
Generator (of semigroup)      14
Harmonic function      9
Hitting probability      102
Hitting time      91
Hunt process      90
Integral of measure      71
Irregular point      93
Ito’s formula      150
Jumping measure      49 119
Kernel      27
Killing inside      114
Killing measure      49 116
Krein extension      54
Lateral condition      59
Levy process      95
Levy — Khinchin formula      29
Life time      89
Lindeberg type condition      95
Local property      6
M-invariant set      91
Markov process      88
Markov property      88
Markovian form      5
Markovian kernel      27
Markovian operator      23
Martingale additive functional      135
Measure (of finite energy integral)      68
Minimum admissible family      88
Minimum completed admissible family      89
Mollifier      7
Mutual energy      136
Nearly Borel measurable      93
Nest      64 145
Newtonian capacity      68 81
Newtonian kernel      40
Newtonian potential      40
Normal Markov contraction      5
Normal Markov process      88
Optional sampling theorem      103
Part (of the Dirichlet form)      111
Part (of the process)      92
Poincare’s inequality      38
Polar set      94
Potential (of measure)      69
Properly exceptional      96
Q.e.      63 98
Quadratic variation      135
Quasi-continuous (in the restricted sense)      64
Quasi-continuous function      64
Quasi-everywhere      63 98
Quasi-left continuity      90
Reduced function      77
Reference function      34
Reflecting barrier Brownian motion      112
Regular boundary      9
Regular form      6
Regular nest      64
Regular point      93
Regular set      79
Reproducing kernel      82
Resolvent (of a linear operator)      14
Resolvent kernel (Markovian)      27
Resurrected form      120
Riesz kernel      39
Riesz potential      39 74
Semi-martingale      151
Semi-martingale decomposition      138
Semi-polar set      94
Semigroup      14
Set (of potential zero)      95
Singular set      47
Smooth measure Sobolev inequality      40
Smooth space (of order 1)      10
Spatially homogeneous Markov process      94
Spectral synthesis      79
Spectrum (of function)      79
Standard process      90
Stochastic integral      156
Stochastic process      88
Stopping time      88
Strong Markov property      89
Supermartingale      103
Support (of additive functional)      149 165
Sweeping out (of additive functional)      132
Sweeping out (of measure)      79
Symmetric (kernel)      27
Symmetric Cauchy process (on the boundary)      170
Symmetric form      3
Symmetric form in the wide sense      21
Symmetric Markov process      95
Symmetric stable process      95
Symmetric stable semigroup      39
Thin set      94
Time changed Dirichlet space      168
Time changed process      166
Transformation rule      161
Transient Dirichlet space      34 35
Transient semigroup      32
Transition function (Markovian)      27
Translation operato      87
Trap      92
Uniform ellipticity      43
Unit contraction      5
Universally measurable set      87
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