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Kolokoltsov V.N. — Semiclassical Analysis for Diffusions and Stochastic Processes
Kolokoltsov V.N. — Semiclassical Analysis for Diffusions and Stochastic Processes

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Название: Semiclassical Analysis for Diffusions and Stochastic Processes

Автор: Kolokoltsov V.N.


The monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition probabilities of various Markov processes. These include (i) diffusions (in particular,degenerate diffusions), (ii) more general jump-diffusions, especially stable jump-diffusions driven by stable Lévy processes, (iii) complex stochastic Schrödinger equations which correspond to models of quantum open systems. The main results of the book concern the existence, two-sided estimates, path integral representation, and small time and semiclassical asymptotics for the Green functions (or fundamental solutions) of these equations, which represent the transition probability densities of the corresponding random process. The boundary value problem for Hamiltonian systems and some spectral asymptotics ar also discussed. Readers should have an elementary knowledge of probability, complex and functional analysis, and calculus.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 368

Добавлена в каталог: 13.05.2008

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Предметный указатель
Belavkin’s quantum filtering equation      Sect. 1.4 Ap.A
Characteristics of a Hamiltonian      Sect. 2.1
Coefficient of the quality of measurement      Sect. 1.4
Courrege’s structure theorem on the generators of Feller processes      Ap.D
Curvilinear Ornstein — Uhlenbeck process      Ch.4
Dimensionality of a measure      Sect. 9.4
Feynman’s path integral      Sect. 7.4 Ch. Ap. H
Focal and conjugate points      Sect. 2.1
Gaussian diffusion long time behavior      Sect. 1.3
Gaussian diffusion rate of escape      Sect. 1.5
Gaussian diffusion structure theory of Chaleyat-Maurel and Elie      Sect. 1.2
Invariant degenerate diffusion on cotangent bundles      Sect. 4.1
Jump-diffusion process      Ap. D
Laplace method for Laplace integrals      Ap. B
Large deviation principle for (complex) stochastic Schrodinger equation      Sect. 7.3
Large deviation principle for diffusions      Sect. 3.5
Large deviation principle for stable jump-diffusion      Sect. 6.2
Levy measure      Sect. 2.5 Ap. D
Maslov’s tunnel equations      Sect. 6.1
Non-stationary perturbation theory      Sect. 9.1
Random wave operators      Sect. 1.5
Regular Hamiltonians      Sect. 2.4
Regular Hamiltonians of the first rank      Sect. 2.3
Regular points of Hamiltonian systems      Sect. 2.2
Saddle-point method (infinite-dimensional)      Sect. 7.4
Scattering theory for stochastic Newton and Schrodinger equations      Sect. 1.5
Semiclassical approximation for complex stochastic diffusions or SSE      Ch. 7
Semiclassical approximation for diffusion      Ch. 3
Semiclassical approximation for Feller processes      Ch. 6
Semiclassical approximation for spectral problems      Ch. 8
Stable processes sample path propertie      Sect. 5.6
Stable processes transition probability densities      Sect. 5.1 5.2
Stochastic geodesic flow      Ch.4
Stochastic Schrodinger equation (SEE)      Sect. 1.4 Ch.7 Ap.
Truncated stable jump-diffusions      Sect. 5.4 Ch.
Two-point function of a Hamiltonian      Sect. 2.1
Two-sided estimates for heat kernel      Sect. 3.4 5.3 7.3
Wiener chaos decomposition      Sect. 9.6
Young schemes      Sect. 1.2 2.4
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