Assing S., Schmidt W.M. — Continuous Strong Markov Processes In Dimension One: A Stochastic Calculus Approach :: Электронная библиотека попечительского совета мехмата МГУ

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Assing S., Schmidt W.M. — Continuous Strong Markov Processes In Dimension One: A Stochastic Calculus Approach

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Название: Continuous Strong Markov Processes In Dimension One: A Stochastic Calculus Approach

Авторы: Assing S., Schmidt W.M.

Аннотация:

The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 135

Добавлена в каталог: 11.01.2010

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Предметный указатель

-admissible measure      82
$S_{\pm}$ -drift function      51
$\mu_{g}$ -integrable function      132
a.s      1
Absorbing points      see Points
Additive functional, perfect      27 79
Additive functional, weakly      28 79
Additive process      see Stochastic process
Admissible measure      see $p$

-admissible measure
Attainable points      see Points
Attracting points      see Points
Component (of )      22
Concave, -concave      53
Connected points      see Points
Filtration      1
Filtration, augmented in      1
Filtration, right-continuous      2
Filtration, time-changed      10
Increasing process      see Stochastic process
Interval connected with respect to       16
It $\hat{o}$ process      112
Left singular points      see Points
Nonattracting points      see Points
Perfect terminal time      4
Points, attainable      22
Points, attracting      22
Points, connected      16
Points, nonattracting      22
Points, of right-increase      28
Points, regular      15

Points, singular      15
Points, singular, absorbing      15
Points, singular, left singular      15
Points, singular, right singular      15
Points, singular, special singular      17
Process      see Stochastic process
Reflected Wiener process      see Wiener process
Regular points      see Points
Regular process      15
Right singular points      see Points
Scale function      22
Semimartingale decomposition      4
Semimartingale function      6
shift operators      2
Singular points      see Points
Special singular points      see Points
Speed measure      62 75
Speed measure, restriction to $S_{+}$       59
Speed measure, restriction to $S_{-}$       59
Speed measure, restriction to $\bar{R}\backslash E$       57
Stochastic integral      4
Stochastic process      1
Stochastic process, additive      4
Stochastic process, increasing      10
Stochastic process, perfect additive      4
Stochastic process, right-inverse      10
Stochastic process, time-changed      10
Time change, $\mathbb{F}$ -time change      10
Wiener process      4
Wiener process, reflected Wiener process      119

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