Semiclassical analysis for diffusions and stochastic processes, Vassili N. Kolokoltsov

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The instance Semiclassical analysis for diffusions and stochastic processes, Vassili N. Kolokoltsov represents a material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.

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Semiclassical analysis for diffusions and stochastic processes, Vassili N. Kolokoltsov

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Vassili N. Kolokoltsov

Instantiates

• Semiclassical analysis for diffusions and stochastic processes

Publication

• Berlin | London, Springer, 2000

Bibliography note

Includes bibliographical references (p. [329]-345) and index

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volume

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• nc

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rdacarrier

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text

Content type code

• txt

Content type MARC source

rdacontent

Contents

• Introduction.
• p. 1
• Ch. 1.
• Gaussian diffusions
• 1.
• Gaussian diffusion. Probabilistic and analytic approaches.
• p. 17
• 2.
• Classification of Gaussian diffusions by the Young schemes.
• p. 20
• 3.
• Long time behaviour of the Green functions of Gaussian diffusions.
• p. 25
• 4.
• Complex stochastic Gaussian diffusion.
• p. 28
• 5.
• rate of escape for Gaussian diffusions and scattering for its perturbations.
• p. 34
• Ch. 2.
• Boundary value problem for Hamiltonian systems
• 1.
• Rapid course in calculus of variations.
• p. 40
• 2.
• Boundary value problem for non-degenerate Hamiltonians.
• p. 50
• 3.
• Regular degenerate Hamiltonians of the first rank.
• p. 59
• 4.
• General regular Hamiltonians depending quadratically on momenta.
• p. 72
• 5.
• Hamiltonians of exponential growth in momenta.
• p. 75
• 6.
• Complex Hamiltonians and calculus of variations of saddle-points.
• p. 87
• 7.
• Stochastic Hamiltonians.
• p. 92
• Ch. 3.
• Semiclassical approximation for regular diffusion
• 1.
• Main ideas of the WKB-method with imaginary phase.
• p. 97
• 2.
• Calculation of the two-point function for regular Hamiltonians.
• p. 104
• 3.
• Asymptotic solutions of the transport equation.
• p. 110
• 4.
• Local asymptotics of the Green function for regular Hamiltonians.
• p. 112
• 5.
• Global small diffusion asymptotics and large deviations.
• p. 119
• 6.
• Asymptotics for non-regular diffusion: an example.
• p. 124
• 7.
• Analytic solutions to some linear PDE.
• p. 128
• Ch. 4.
• Invariant degenerate diffusion on cotangent bundles
• 1.
• Curvilinear Ornstein-Uhlenbeck process and stochastic geodesic flow.
• p. 136
• 2.
• Small time asymptotics for stochastic geodesic flow.
• p. 140
• 3.
• trace of the Green function and geometric invariants.
• p. 143
• Ch. 5.
• Transition probability densities for stable jump-diffusion
• 1.
• Asymptotic properties of one-dimensional stable laws.
• p. 146
• 2.
• Asymptotic properties of finite-dimensional stable laws.
• p. 149
• 3.
• Transition probability densities for stable jump-diffusion.
• p. 161
• 4.
• Stable jump-diffusions combined with compound Poisson processes.
• p. 178
• 5.
• Stable-like processes.
• p. 182
• 6.
• Applications to the sample path properties of stable jump-diffusions.
• p. 187
• Ch. 6.
• Semiclassical asymptotics for the localised Feller-Courrege processes
• 1.
• Maslov's tunnel equations and the Feller-Courrege processes.
• p. 191
• 2.
• Rough local asymptotics and local large deviations.
• p. 194
• 3.
• Refinement and globalisation.
• p. 217
• Ch. 7.
• Complex stochastic diffusions or stochastic Schrodinger equations
• 1.
• Semiclassical approximation: formal asymptotics.
• p. 223
• 2.
• Semiclassical approximation: justification and globalisation.
• p. 229
• 3.
• Applications: two-sided estimates to complex heat kernels, large deviation principle, well-posedness of the Cauchy problem.
• p. 235
• 4.
• Path integration and infinite-dimensional saddle-point method.
• p. 236
• Ch. 8.
• Some topics in semiclassical spectral analysis
• 1.
• Double-well splitting.
• p. 239
• 2.
• Low lying eigenvalues of diffusion operators and the life-times of diffusion processes.
• p. 247
• 3.
• Quasi-modes of diffusion operators around a closed orbit of the corresponding classical system.
• p. 252
• Ch. 9.
• Path integration for the Schrodinger, heat and complex stochastic diffusion equations
• 1.
• Introduction.
• p. 255
• 2.
• Path integral for the Schrodinger equation in p-representation.
• p. 263
• 3.
• Path integral for the Schrodinger equation in x-representation.
• p. 267
• 4.
• Singular potentials.
• p. 269
• 5.
• Semiclassical asymptotics.
• p. 272
• 6.
• Fock space representation.
• p. 276
• App. A.
• Main equation of the theory of continuous quantum measurements.
• p. 280
• App. B.
• Asymptotics of Laplace integrals with complex phase.
• p. 283
• App. C.
• Characteristic functions of stable laws.
• p. 293
• App. D.
• Levy-Khintchine [Psi]DO and Feller-Courrege processes.
• p. 298
• App. E.
• Equivalence of convex functions.
• p. 303
• App. F.
• Unimodality of symmetric stable laws.
• p. 305
• App. G.
• Infinite divisible complex distributions and complex Markov processes.
• p. 312
• App. H.
• review of main approaches to the rigorous construction of path integral.
• p. 322
• App. I.
• Perspectives and problems.
• p. 326
• References.
• p. 329
• Main notations.
• p. 346
• Subject Index.
• p. 347

Control code

l80000026545

Dimensions

24 cm.

Extent

viii, 345 p.

Isbn

9783540669722

Lccn

lc00026545

Media category

unmediated

Media MARC source

rdamedia

Media type code

• n

Other physical details

ill.

Record ID

b1948076