Stochastic and asymptotic analysis applied to the study of stochastic models of classical and quantum machanics

Tyukov, A.E., 2001. Stochastic and asymptotic analysis applied to the study of stochastic models of classical and quantum machanics. PhD, Nottingham Trent University.

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Abstract

Applying WKB method we obtain multiplicative small time and semiclassical asymptotics for Green functions (fundamental solutions) and for the solutions of Cauchy problem for the stochastic heat equation driven by a Levy noise. The relevant theory of stochastic Hamilton systems and Hamilton-Jacobi equations is developed.

We also give conditions for non-explosion of solutions of Newton systems driven by a Levy noise and conditions for transience of solutions of such systems driven by a-stable noise. As a solution of particular Newton system we consider a-stable Ornstein-Uhlenbeck process for which we estimate the rate of escape. The connections between the objects studied in this theses are shown on the scheme at page V.

Item Type:	Thesis
Creators:	Tyukov, A.E.
Date:	2001
ISBN:	9781369325768
Identifiers:	Number Type PQ10290327 Other
Divisions:	Schools > School of Science and Technology
Record created by:	Laura Ward
Date Added:	08 Jul 2021 09:18
Last Modified:	22 May 2024 14:38
URI:	https://irep.ntu.ac.uk/id/eprint/43373

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