Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Dynkin E. — An Introduction to Branching Measure-Valued Processes
Dynkin E. — An Introduction to Branching Measure-Valued Processes

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: An Introduction to Branching Measure-Valued Processes

Автор: Dynkin E.

Аннотация:

For about half a century, two classes of stochastic processes — Gaussian processes and processes with independent increments — have played an important role in the development of stochastic analysis and its applications. During the last decade, a third class — branching measure-valued (BMV) processes — has also been the subject of much research. A common feature of all three classes is that their finite-dimensional distributions are infinitely divisible, allowing the use of the powerful analytic tool of Laplace (or Fourier) transforms. All three classes, in an infinite-dimensional setting, provide means for study of physical systems with infinitely many degrees of freedom. This is the first monograph devoted to the theory of BMV processes. Dynkin first constructs a large class of BMV processes, called superprocesses, by passing to the limit from branching particle systems. Then he proves that, under certain restrictions, a general BMV process is a superprocess. A special chapter is devoted to the connections between superprocesses and a class of nonlinear partial differential equations recently discovered by Dynkin.


Язык: en

Рубрика: Математика/Вероятность/Стохастические процессы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 74

Добавлена в каталог: 28.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$R_{D}$-polar set      5
$\hat{\psi}$-superprocess      20
$\phi$-localization      84
$\xi$-martingale      27 38
Additive function      38
Additive function, adapted      38
Additive function, right continuous (RCA)      38
Additive functional      31
Additive functional, admissible      49
Additive functional, characteristic of      31
Additive functional, continuous      31
Additive functional, corresponding to an exit rule      85
Additive functional, equivalent      31
Additive functional, linear (LAF)      18 82
Additive functional, measure-valued (MVAF)      35
Additive functional, natural      31
Additive functional, signed      31
Additive martingale      38
Additive martingale, continuous      40
Additive martingale, measure-valued      40
Additive martingale, purely discontinuous      40
Additive martingale, square integrable      39
Admissible metric      98
Admissible metric, special      101
Associated linear semigroup      11
Augmentation      116
Baras, P.      i
Base space      9
Base space, finite      19 109
Base space, one point      21 109
Bessel capacity      4
Branching measure-valued (BMV) process      9
Branching measure-valued (BMV) process, critical      17
Branching measure-valued (BMV) process, deterministic      10
Branching measure-valued (BMV) process, subcritical      17
Branching measure-valued (BMV) process, supercritical      17
Branching particle system      46
Branching property      9
Branching property, strong      109
Branching property, week      109 110
Branching, $\alpha$-brancing      16
Branching, binary      16
Branching, characteristic of      17
Branching, continuous      10
Branching, discontinuous      10
Branching, local      16
Branching, quadratic      16
Brezis, H.      i 2
Brownian motion      28
Capacity      3
Characteristic of continuous branching      17
Characteristic of discontinuous branching      17
Class (D)      115
Compensator      39 40 85 117
Continuous martingale part of $\langle f^{t}, X_{t} \rangle$      86
Continuous martingale part of X      121
Courant, R.      1
Critical case      i
Critical Hausdorff dimension      4
Dawson — Watanabe superprocess      16 112
Dawson, D.A.      i 10 112
Diffusion      25
Diffusion, Feller's      10
Diffusion, generator of      28
Dirichlet problem      1
Dmitriev, N.A.      109
Doob — Meyer decomposition      39 116
Doob, J.L.      5
El Karoui, N.      114
Exit rule      29 80
Exit rule, signed (SER)      29
Extinct cloud      2
Feller's diffusion      10
Feller, W.      109
Feynman — Kac formula      14 63
Feynman — Kac formula, classical      67
Filtered space      27 115
Filtration      115
Fine topology      28
Finely open set      22
Fitzsimmons, P.J.      77 112
Friedman, A.      i
Friedrichs, R.      1
Function, adapted to $\xi$      38
Function, adapted to $\xi$, finely continuous      28
Function, adapted to $\xi$, invariant      80
Function, adapted to $\xi$, L-continuous      28
Function, adapted to $\xi$, nearly Borel      27 37
Function, adapted to $\xi$, of finite variation      120
Function, adapted to $\xi$, R-continuous      28
Function, adapted to $\xi$, RL-continuous      28
Function, adapted to $\xi$, special (SP)      29
Functional, admissible      49
Functional, admissible, generating      45
Functional, admissible, Laplace      50
Galton — Watson process      109
Gmira, A.      5
Hausdorff dimension      4
Hunt process      28
Hunt, G.A.      5
Infinitely-divisible distribution      12
Ito's formula      122
Jirina, M.      109
Kakutani, S.      1
Kernel      14 52
Kernel, stochastic      45
Kernel, Substochastic      46
Killing      14
Kolmogorov, A.N.      109
Kuznetsov, S.E.      77 112
L-continuity      81
Lamperti, J.      109 110
Laplace equation      1
Laplace functional      50
Laplace transform      12
Le Gall, J.F.      i 5 7 112
Levy measure      41 71
Levy measure, modified      41
Levy — Khinchin formula      12
Levy, P.      1
Lifting      82
Linear additive functional (LAF)      82
localization      49 84
Loewner, C.      i 1
Log-Laplace differential equation      20
Log-Laplace equation      10
Log-Laplace semigroup      10
Luzin space      27
Markov process      26
Markov process in a finite state space      19
Markov process with mass creation      16
Markov property      27
Markov semigroup      26
Martin boundary      5
Martingale      115
Martingale measure      117
Martingale over $\xi$      38
Martingale, $\xi$-adapted      38
Martingale, local      120
Martingale, locally square integrable      120
Martingale, purely discontinuous      118
Measure-valued additive functional (MVAF)      35
Mokobodzki, G.      34
Nirenberg, L.      i 1
Partition of unity      102
Perkins, E.A.      i 112
Pierre, M.      i
Poisson kernel      4
Poisson measure      45
Polar set      3
Process of quadratic variation      118
Process with mass creation      16
Process, $\xi$-predictible      27
Process, adapted      115
Process, bounded      121
Process, branching      9
Process, conservative      10
Process, indistinguishible      115
Process, locally bounded      121
Process, optional      115
Process, predictible      115
Process, progressively measurable      115
Process, quasi-left continuous      28 115
Process, right      27
Process, split-time      29
Projection      17 18 82
Purely discontinuous martingale part of $\langle f^{t}, X_{t} \rangle$      86
Quadratic variation process      118
R-continuity      81
R-polar set      3
r-stopping time      27
Radon — Nikodym theorem      36
Random field      22
Range of $\xi$      3
Range of X      3
Reconstructable $\sigma$-algebra      27
Right continuous additive function (RCA)      38
Roelly, S.      114
Rost theorem      44
Semigroup, linear associated with X      11
Semigroup, log-Laplace      10
Semigroup, Markov      26
Semimartingale      120
Sheu, Y.C.      ii 5
Signed exit rule      29
Silverstein, M.L.      109 110 111
Special function      29
Standard sequence of partitions      117
Stochastic integral      120 121
Stopping distribution      43
Stopping time      81 115
Stopping time, predictible      116
Stopping time, randomized      43
Strong Markov property      27
Stroock, D.W.      113
Subcritical case      i
Submartingale      115
Submartingale measure      117
Subprobability      25
Super-Brownian motion      16
Superdiffusion      21
Superdiffusion, time-homogeneous      24
Supermartingale      115
Supermartingale measure      117
Superprocess      14 49
Superprocess as a random field      22
Superprocess with parameters $(\xi, K, \psi)$      49
Superprocess, enhanced      23
Superprocess, time-homogeneous      16
Total family      93
Total mass process      80 82
Transition function      25
Universal completion      29
Usual hypotheses      16
Varadhan, S.R.S.      113
Veron, L.      i 2 5 7
Watanabe, S.      110 112
Watson, H.W.      109
X-martingale      80
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте