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Dynamic theory of stochastic movement of systems


Nagasawa, M (2007). Dynamic theory of stochastic movement of systems. In: Jensen, B S; Palokangas, T. Stochastic economic dynamics. Frederiksberg: Copenhagen Business School Press, 133-164.

Abstract

The author studies the dynamic theory of stochastic processes. The dynamic theory concerns an evolution
equation which contains a potential function , and the diffusion matrix and drift vector. The case with no
potential term can be treated in the framework of the conventional theory of Markov processes of Kolmogorov
and Itˆo, which is a kinematic theory. The kinematic equation determines Markov (diffusion) processes, i.e.,the
movement of systems. By contrast, the author considers the equation of motion in the mechanics part of the
dynamic theory. The equation of motion contains the potential function of external forces. External forces
influence the movement of systems, but not in a direct way. The kinematic equation finally describes sample
paths of the movement of observing systems. In this paper the author clarifies the mathematical structures
which connect three notions, external force, induced drift vector and sample paths of the movement.

Abstract

The author studies the dynamic theory of stochastic processes. The dynamic theory concerns an evolution
equation which contains a potential function , and the diffusion matrix and drift vector. The case with no
potential term can be treated in the framework of the conventional theory of Markov processes of Kolmogorov
and Itˆo, which is a kinematic theory. The kinematic equation determines Markov (diffusion) processes, i.e.,the
movement of systems. By contrast, the author considers the equation of motion in the mechanics part of the
dynamic theory. The equation of motion contains the potential function of external forces. External forces
influence the movement of systems, but not in a direct way. The kinematic equation finally describes sample
paths of the movement of observing systems. In this paper the author clarifies the mathematical structures
which connect three notions, external force, induced drift vector and sample paths of the movement.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Stochastic process; dynamic theory; kinematic equation; Markov process
Language:English
Date:2007
Deposited On:02 Nov 2009 12:22
Last Modified:05 Apr 2016 13:23
Publisher:Copenhagen Business School Press
ISBN:978-87-630-0185-4
Official URL:http://www.cbspress.dk/Visning-af-titel.848.0.html?&cHash=e17895b8b3&ean=9788763001854
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2405743

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