Blumenthal R.K., Getoor R.M. — Markov processes and potential theory :: Электронная библиотека попечительского совета мехмата МГУ

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Blumenthal R.K., Getoor R.M. — Markov processes and potential theory

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Название: Markov processes and potential theory

Авторы: Blumenthal R.K., Getoor R.M.

Аннотация:

This graduate-level text explores the relationship between Markov processes and potential theory, in addition to aspects of the theory of additive functionals. Topics include Markov processes, excessive functions, multiplicative functionals and subprocesses, and additive functionals and their potentials. A concluding chapter examines dual processes and potential theory.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 325

Добавлена в каталог: 15.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\pi$ -system      5
Accessible stopping time      172
Adapted to      11
Additive functional      147 148
Additive functional of (X,M)      148
Additive functional of X      149
Additive functional of(X,T)      149
Additive functional, continuous      152
Additive functional, equivalence of      149
Additive functional, natural      153
Additive functional, perfect      149 169 205
Additive functional, strong      151
Almost surely      27
Balayage      136
Balayage of additive functionals      229
Brownian motion      18 51 71 73 83 84 88 94 146 227
Canonical subprocess      107
Capacitary measure      285
Capacity      53
Capacity, capacitable      54
Capacity, natural capacity      285
Characteristic of an additive functional      159
co- (as a prefix)      259
Completion (with respect to a family of measures)      26
d-system      5
Doob’s theorem      81
Entry time      52
Exactly subordinate      117
Excessive function      72
Excessive function, $\alpha-V$ excessive      115 252
Excessive function, (X,M) excessive      125
Excessive function, admissible      277
Excessive function, regular      187 287
Excessive function, uniformly      169
Excessive function, uniformly integrable      187
Excessive measure      257
Excessive regularization      78 116
Exit set      235
Exit set, strong      240
Exponent of a subordinator      219
Feller process (strong)      77
Fine topology      85
Fine topology, closure      87 199
Fine topology, support of a continuous additive functional      204 213
Fine topology, support of a measure      204
Gauss kernel      18
Harmonic function      187
Harmonic measure      61
Hitting distribution      61
Hitting distribution, time      52
Holding point      91
Hunt process      45
Independent increments      17 51 52 219 264 290
Initial distribution      15
Instantaneous point      91
Inverse of an additive functional      208
Inverse of an increasing function      207
Irregular      61 80 199
Levy measure      219
Lifetime      22
Local time      216 293 294
Local time on a set      232
Locally integrable      266
Markov kernel      63
Markov process      11
Markov process in duality      259
Markov process of function space type      24
Markov process with transition function      15
Markov process with translation operators      20
Markov process, equivalence of      24
Markov process, right continuous      41
Markov process, temporally homogeneous      15
Measurable stochastic process      34
Measurable stochastic process, progressively      34
Monotone class theorem      5 6 7
Multiplicative functional      97
Multiplicative functional, equivalence of      98
Multiplicative functional, exact      120

Multiplicative functional, normalized      124
Multiplicative functional, perfect      149
Multiplicative functional, regular      119
Multiplicative functional, right continuous      98
Multiplicative functional, strong      110
Nearly Borel set      59
Nearly supermedian      267
Normal Markov process      30
Null set      79
Path      21
Permanent point for a multiplicative functional      98
Permanent point for a semigroup      102
Poisson process      19 20
Polar set      79
Potential natural      178
Potential Newtonian      71
Potential of a function      41 69
Potential of a measure      254 257
Potential of an additive functional      154
Potential, pseudo      187
Potential, regular      161
Potential, Riesz      71
Potential, theory (classical)      94
Potential, zero (set of)      79
Projective system      16
Projective system, set      229
Quasi-left-continuous      45
Quasi-left-continuous on $[0,\infty)$       45
Quasi-left-continuous on $[0,\zeta)$       45
Recurrence      88 89
Reduite      136
Reference measure      196
Regular point      61 199
Regular point, step process      63 91 264
Resolvent      41 252
Resolvent in duality      253
Resolvent, equation      41
Resolvent, exactly subordinate      117
Resolvent, subordinate      115
Riesz decomposition      272 279
Right continuous family of $\sigma$ -algebras      31
Semigroup generated by a multiplicative functional      100
Semigroup generated by a multiplicative functional, subordinate      101
Semipolar set      79
Special set      133
Stable process      293
Stable process, one-sided      19 71 227 264 294
Stable process, symmetric      19 71 83 264
Standard process      45
State space      20
Stochastic process      11
Stochastic process, adapted to a family of $\sigma$ -algebras      11
Stopping time      31
Stopping time for X      36
Strong Markov property      37 38
Strong Markov property for an additive functional      151
Strong order      190
Subordinator      219
Subprocess      105
Super-mean-valued      77 81
Superharmonic      96
Supermartingale      4
Supermedian      115 252
Support of a continuous additive functional      213
Terminal time      78 98
Terminal time, complete      173
Terminal time, exact      124
Terminal time, perfect      153
Terminal time, strong      124
Thin set      79
Thin set at a point      79
Time changed process      212 228 232 233
Transition function      14
Transition function, sub-Markov      22
Transition function, temporally homogeneous      14
Translation operators      21
Uniform motion      23
Zero-one law      30

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