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Port S.C., Stone C.J. — Brownian motion and classical potential theory
Port S.C., Stone C.J. — Brownian motion and classical potential theory



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Название: Brownian motion and classical potential theory

Авторы: Port S.C., Stone C.J.

Аннотация:

The importani and beautiful connection between Brownian motion and classical potential theory was first investigated by Kakutani, Kac, and Doob. Hunt then showed that potential theory could be developed by probabilistic methods for a large class of transient Markov processes. There is now a large literature on potential theory for transient Markov processes, including books by Dynkin, ltd and McKean, Meyer, and Blumenthal and Getoor. Recurrent potential theory was first developed for random walks by Spitzer and for Markov chains by Kemeny and Snell. Further work in this area has been done by a number of people, including the present authors Port and Stone and Stone(see books by Spitzer, Kemeny, Snell and Knapp, and Revuz).
In spite of the large amount of written material on probabilistic potential theory, the connection between Brownian motion and classical potential theory remains largely inaccessible to nonexperts. The purpose of this book is to give an account of this connection, accessible to readers familiar with real variable theory and probability theory as usually developed at the graduate level (a knowledge of Chung should suffice). No prior knowledge of either Brownian motion or classical potential theory is assumed...


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 246

Добавлена в каталог: 30.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Almost everywhere      17
Averaging property      85
Balayage problem, Green potential      172
Balayage problem, logarithmic potential      212
Barrier      140
Blumenthal's zero-one law      8
Borel-Cantelli lemma, extended      65
Boundary value      87
Capacitability theorem      11 204 227
Capacity, $\lambda$      42
Capacity, Green      190
Capacity, Green, inner      203
Capacity, Green, outer      203
Capacity, logarithmic      80
Capacity, logarithmic, inner      226
Capacity, logarithmic, outer      226
Capacity, Newtonian      57
Cauchy density      29
Cauchy sequence      183
Cauchy sequence, weak      183
Charge      44
Complete maximum principle      210
Condenser measure, Green potential      194
Condenser measure, logarithmic potential      219
Condenser theorem, Green potential      195
Condenser theorem, logarithmic potential      219
Cone      26
Cone, condition for recurrence      26
Cone, condition for regularity      30
Continuity principle, Green potential      163
Continuity principle, logarithmic potential      207
Contraction mapping      223
Convergence, complete      18
Convergence, strong      183
Convergence, vague      18
Convergence, weak      183
Dirichlet principle      88
Dirichlet problem      88
Dirichlet problem, exterior      90
Dirichlet problem, generalized      90
Dirichlet problem, stochastic      154
Dirichlet space      195
Domination principle      175
Eigenfunction      122
Eigenvalue      122
Energy principle, Green potential      181
Energy principle, logarithmic potential      214
Energy, Green potential      180 182
Energy, Green potential, mutual      181
Energy, logarithmic potential      213
Equilibrium charge distribution      204
Equilibrium measure, $\lambda$-potential      42
Equilibrium measure, Green potential      190
Equilibrium measure, linear potential      84
Equilibrium measure, logarithmic potential      76
Equilibrium measure, Newtonian potential      57
Equilibrium potential, $\lambda$      42
Equilibrium potential, Green      190
Equilibrium potential, linear      84
Equilibrium potential, logarithmic      76
Equilibrium potential, Newtonian      57
Equilibrium problem, Green potential      190
Equilibrium problem, logarithmic potential      213
Event      2
Exit distribution      88
Exit time      40
Exit time, last      23 200
Function, boundary      87
Function, concave      129
Function, continuous      16
Function, continuous, essentially      89
Function, continuous, extended sense      16
Function, continuous, Hoelder      115
Function, excessive      135
Function, Green      111
Function, harmonic      85
Function, locally integrable      85
Function, reduced      176
Function, resolutive      148
Function, semicontinuous, lower      19
Function, semicontinuous, upper      19
Function, subharmonic      128
Function, superharmonic      128
Function, superinvariant      135
Fundamental identity, $\lambda$-potential      41
Fundamental identity, Green potential      161
Fundamental identity, linear potential      83
Fundamental identity, logarithmic potential      71
Fundamental identity, Newtonian potential      55
Generalized      114
Harmonic continuation      107
Harmonic minorant      140
Harmonic minorant, greatest      140
Harnack's inequality      104 105
Harnack's theorem      105
Hitting distribution      28 160
Hitting distribution, starting at infinity      77
Hitting time      10
Hyperplane      29
Invariance, orthogonal      5
Invariance, scale      5
Invariance, translation      5
inversion      100
Karamata's Tauberian theorem      126
Kelvin transformation      101
Kolmogorov Extension Theorem      3
Laplacian      86
Laplacian, generalized      114
Limit at infinity      93
Lower class      146 148
Lower regularization      129
Markov property      7
Markov property, strong      12
Maximum principle, $\lambda$-potential      42
Maximum principle, Green potential      163
Maximum principle, logarithmic potential      207
Measure, Radon      17
Measure, Radon, signed      181
Measure, restriction      160
Measure, set of concentration      17
Measure, support      17
Monotone class theorem      5
Normal density      1
Point, cutoff      47
Point, irregular      30
Point, of thinness      141
Point, regular      30
Point, regular, for Dirichlet problem      89
Poisson equation      114
Poisson integral formula      104
Poisson integral representation      108
Potential      19
Potential, $\lambda$      41
Potential, Green      157
Potential, linear      82
Potential, logarithmic      71
Potential, Newtonian      54
Process, recurrent      25
Process, transient      25
PWB method      145
Quasi-e very where      174 204
Random variable      2
Reduite      176
Riesz decomposition theorem, Green potential      168
Riesz decomposition theorem, logarithmic potential      208
Robin constant, linear potential      84
Robin constant, logarithmic potential      76
Semigroup property      1 18
Set, ${F}_{\sigma}$      11
Set, ${H}_{D}$-null      88
Set, capacitable, Green potential      203
Set, capacitable, logarithmic potential      226
Set, complete      186
Set, complete, weakly      186
Set, dense      184
Set, equilibrium      190
Set, Greenian      111
Set, nonpolar      20
Set, polar      20 144
Set, recurrent      24
Set, regular      89
Set, relatively compact      90
Set, starshaped      27
Set, starshaped, strongly      98
Set, thin      141
Set, transient      24
Set, transient, relatively      200
Shift transformation      7
Stopping time      8
Terminal time property      11
Thinness      141
Thorn      68
Transition operator, Brownian motion on open set      40
Transition operator, killed Brownian motion      33
Uniform probability distribution      16
Uniqueness principle, Green potential      175
Uniqueness principle, logarithmic potential      73 211
Uniqueness principle, Newtonian potential      55
Upper class      146 148
Wiener's test      66 96 145 225
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