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Dynkin E.B., Yushkevich A.A. — Markov processes; theorems and problems
Dynkin E.B., Yushkevich A.A. — Markov processes; theorems and problems

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Название: Markov processes; theorems and problems

Авторы: Dynkin E.B., Yushkevich A.A.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 244

Добавлена в каталог: 11.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\varepsilon$ — Neighborhoods      50
2-Row phase space      127
Absorbing boundary      180 200
Absorption      75 160 147
Absorption, coefficient      190
Accessible boundary      173 197
Accession of points in optimal choice      90
Analysis and Markov processes, v      38
Attracting boundary      161 173
Birth and death process      151 154 164
Birth and death process, continued      174 189 200
boundary conditions      147 148 176 198
Boundary points (regular and irregular)      51 59 148 176 216
Boundary, absorbing      180 200
Boundary, accessible      173 197
Boundary, attracting      161 173
Boundary, classification of types      173 211
Boundary, finite      211
Boundary, inaccessible      173
Boundary, inward passable      196
Boundary, irregular      59
Boundary, nonabsorbing      217
Boundary, regular      51 54
Boundary, repelling      161 173
Boundary, strongly finite      211
Boundary, weakly finite      211
Brownian motion      41 52 65
Canonical coordinate      157
Cantor perfect set      196
Capacity      17 36
Capacity, definition      18
Carrier of set      35
Cauchy distribution      61
Cayley lottery problem      131
Characteristic operator      72 147
Characteristic operator, “class A” processes      176 189 209
Characteristic, birth and death processes      167
Characteristic, infinitesimal      69
Charge      18
Charge, maximum total      19
Chebyshev inequality      181
Choquet theorem      141
Circular domain      44 64
Compacmm      37 138
Compact convex sets      32 37
Concave function      113 122 225
Concave function, fundamental property      119
Conditional expectation of first-exit time      178
Conditional probability      88 92 96 213
Continuations of birth and death process      174 189 200
Continuous analog of symmetric random walk      113
Continuous random walk      39 113 233
Cumulative jump (transition) time      154 170
Decision      87 90
Denumerable Markov chain      119 136
Denumerable phase space      109 136
Derivative on a measure      170
Difference function      121
Diffusion processes      74 147 155 178
Dirichlet problem      33 48 60 114
Dirichlet problem, probabilistic treatment      vi
Discrete potential      11 28 103
Distribution at time of exit from circle      43
Distribution, $\mu$-distribution of Wiener process      42
Distribution, Cauchy      67
Distribution, equilibrium      18
Distribution, limiting      40
Distribution, normal      40
Distribution, normed-sum      39
Distribution, Poisson      218
Domination principle      35
Double-row phase space      127
Elliptic operator L (diffusion process)      74
Envelope principle      35
Equilibrium distribution      18
Equilibrium potential      18
Escape probability      66 155 158
Escape probability from arbitrary domain      47
Escape probability from circle      43
Escape probability, harmonicity of      47
Escape probability, one-dimensional      75
Events (past, current, and future)      56
Excessive functions      15 36 102 138
Excessive functions, definition for multidimensional Wiener process      126
Excessive functions, denumerable Markov chain      136
Excessive majorant of payoff function      111 134
Exit time from arbitrary domain      84
Exit time from circle      43
Exit time from interval      164 210
Expectation (mathematical)      5 100 163 176
Expectation (mathematical), asymptotic expression      7 221
Expectation (mathematical), conditional, of first-exit time      178
Expectation (mathematical), incompletely defined random variables      41
Expectation (mathematical), limit of argument      169
Expectation (mathematical), number of hits at a point      5
Expectation (mathematical), sojourn time      195
Extinction      147 181
Extinction, coefficient      199
Extinction, probability      92
Extremal compact subset of set      31
Extremal points of set      31 37 141 143
Fee fa a game      134
Finite boundary      211
Finite Markov chain      92 100
Finite phase space      92 100
Fluid flow in a plane      70
Free group      142
Fubini’s Theorem      204
Game theory      100 134
General Markov chain      133
Generator of diffusion process (elliptic operator)      74
Green's formula      222
Green's function      136 222
Group (free)      142
Harmonic functions      7 37 60
Harmonic functions, bounded      8
Harmonic functions, definition      7
Harmonic functions, extended definition      136
Harmonic functions, nonnegative      15 61
Harmonic functions, positive      32 144
Helly theorem      139
Homogeneous Markov chain      91
HQ lder continuity      74
Inaccessible boundary      173
Induction (retrograde)      95 131 132
Infinite Markov chain      108
Infinite phase space      108
Infinitesimal operator      70
Inward passability (impassability) of boundary      196
Irregular boundary points      51 59
Jacobian      49 224
Jump measure      182 184
Jump probability      92 212
Laplace equation      18 62 114
Laplace operator      8 73 147 177 222
Laplace operator and Wiener processes      69 171
Lattice      2 19 30
Lattice parameter      39
Lattice “one-dimensional”      100
Left reflection      75
Linear functions      122
Local time      216
Lottery problem      131
Majorizadon of payoff function      105
Mapping of continuous functions into continuous functions (operator)      205
Markov chain      91 156
Markov chain, denumerable      119 136
Markov chain, general      133
Markov chain, homogeneous      91
Markov chain, infinite states      108
Markov chain, recurrent      101
Markov processes      201 (see also Birth and death process “Class Diffusion Markov Random Wiener
Markov processes, relationship to Dirichlet problem      vi
Markov property      46 70 120 148 152 202
Markov times      47 100 103 134 205 217
Martin boundary      136 143
Martin kernel      137
Maximal points (in selection problem,)      89
Mean exit time from arbitrary domain      84
Mean exit time from circle      43 84
Measurability considerations      42 49 114 126
Measure      41 50 137 139 170 182
Multidimensional random walk      2 40
Multidimensional Wiener process      118 1 26
Multiple-row phase space      129
Newtonian potential      11 17
Nonabsorbing boundary      217
Nondifferentiability of Wiener path      81
Nonrecurrent (transient) random walk      2
Nonrecurrent set      16
Normal distribution      40
Normed-sum distribution      39
One-dimensional random walk      1
One-parameter subgroups      121
One-step shift operator      7 103 121
Operators      69 73 121
Operators, characteristic      72 147
Operators, elliptic      74
Operators, infinitesimal      70
Operators, Laplace      8 69 147 171 177 222
Operators, mapping of continuous functions      205
Operators, one-step shift      7 103 121
Operators, resolvent, of process      203
Operators, velocity field      70
Operators, weak infinitesimal      71
Optimal choice problem      87 110
Optimal choice problem further generalization(s) of n “best” objects      129
Optimal stopping problem      87
Optimal stopping problem, general Maikov chain      133
Optimal stopping problem, Markov chain      98
Optimal stopping problem, sequence of independent (dependent) random variables      131
Optimal stopping problem, Wiener process      112
Optimal strategy      107
Path of particle in Brownian motion      41 52 65
Path of particle in random walk      5 22
Path of particle in Wiener process      41 81
Payoff function      14
Payoff function, bounded      101 105 127
Payoff function, unbounded      135
Phase space      155
Phase space, denumerable      109 136
Phase space, double-row      127
Phase space, finite      92 100
Phase space, infinite      108
Phase space, s-row      129
Plausible hypothesis      107
Poisson distribution      218
Poisson equation      171
Poisson equation, probabilistic solution      68
Poisson flow      218 219
Poisson integral      68 84
Potential      11
Potential, $\alpha$-potentials      123
Potential, discrete      11 28 103
Potential, equilibrium      18
Potential, extended definition      136
Potential, Newtonian      11 17
Potential, probabilistic interpretation      12
Probabilistic solution of equations      39
Probability in analysis      39 147
Probability of continued birth and death process      175
Probability of given state at first-exit time from interval      158
Probability of independent events      58
Probability of no return to starting point      63
Probability of random walk event      2
Probability of rated objects      88
Probability of success (payoff)      88 93 102 129
Probability of visit to set after nth step      7 16
Probability of visit to set infinitely often after first step      10
Probability total      1 12 94
Probability transition      3 42 46 92
Probability, conditional      88 92 96 213
Probability, escape      (see Escape probability)
Probability, extinction      92
Probability, jump      92 212
Random walk on a free group with finite number of generators      142
Random walk on a lattice      2 30 39 60 98 100 103 151
Random walk on phase space      92
Random walk one-dimensional      1
Random walk with absorption      110
Random walk, continuous      39
Random walk, continuous analog of symmetric      113
Random walk, multidimensional      2 40
Random walk, nonrecurrent (transient)      2
Random walk, recurrent      2
Random walk, symmetric      1 103 113
Random walk, unsymmetric      37
Rebound at boundary      148
Recurrence of coordinate plane      25
Recurrence of Markov chain      101 162
Recurrence of sets      1 64
Recurrence on axis      25
Recurrence, alternate definition      10 21
Recurrence, criterion      19
Recurrence, definition      2
Recurrent set      16 (see also Recurrence)
Reflecting barrier      211
Reflection      75 147 214
Reflection time      214
Reflection, coefficient      182 184 190
Reflection, “x-reflection”      214 220
Regular boundary points      51 59
Regularity      51 56 59
Regularity, necessary and sufficient conditions      82
Regularity, strong sufficient condition      83
Repelling boundary      161 173
Resolvent (operator)      203
Retrograde induction      95 131 132
Right reflection      76
s-Row phase space      129
Selection problem      (see Optimal choice problem)
Selection strategy (optimal)      88 100
Selection strategy (optimal), table      97
Self-similariiy of Wiener process      44
Sets, $\varepsilon$-support      109 119 134 135
Sets, Cantor perfect      196
Sets, compact convex      32 37
Sets, convex      31 141
Sets, nonrecurrent      16
Sets, recurrent      16
Sets, support      107 129 131
Sets, unpredictable      69
Sets, “sparse” on lattice      64
Sojourn time in state      165 184 194
stopping      87 95 112 131
Stopping, instantaneous      106
Strong Markov properly      46 124 177 203 212
Success (payoff) probability      5 88 93 102 129
Successive approximations, method of      134
Superharmonic functions      8 119 126
Superharmonic functions, definition      8
Superharmonic functions, nonnegative      15
Support set      107 129 131
Support set, $\varepsilon$-support set      109 119 134 135
Sweeping-out principle      35
Symmetric random walk      1 103 113
Time of first exit from circle      61
Time of first exit from zero      54
Time of first visit to circle      81
Time of first visit to layer      24
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