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Port S.C., Stone C.J. — Brownian motion and classical potential theory
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Название: Brownian motion and classical potential theoryАвторы: 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).
Язык: Рубрика: Физика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1978Количество страниц: 246Добавлена в каталог: 30.10.2010Операции: Положить на полку |
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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, 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, 42 Equilibrium measure, Green potential 190 Equilibrium measure, linear potential 84 Equilibrium measure, logarithmic potential 76 Equilibrium measure, Newtonian potential 57 Equilibrium potential, 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, 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, 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, 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, 11 Set, 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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