Technical Semiclassical Analysis for Diffusions and Stochastic Processes (3540669728)

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Vassili N. Kolokoltsov, "Semiclassical Analysis for Diffusions and Stochastic Processes"

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.

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	Science/Engineering Applied Stochastic Processes and Control for Jump-Diffusions: Modeling, Analysis, and Computation Applied Stochastic Processes and Control for Jump-Diffusions: Modeling, Analysis, and Computation (Advances in Design and Control): Floyd B. Hanson Society for Industrial and Applied Mathematics \| ISBN: 0898716330 \| October 3, 2007 \| djvu ...
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