On spatial mutation-selection models

Journal Article · Fri Nov 15 00:00:00 EST 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4828856· OSTI ID:22251419

Kondratiev, Yuri ^[1]; Kutoviy, Oleksandr ^[1]; Minlos, Robert; Pirogov, Sergey ^[2]

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1. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld (Germany)
2. IITP, RAS, Bolshoi Karetnyi 19, Moscow (Russian Federation)

We discuss the selection procedure in the framework of mutation models. We study the regulation for stochastically developing systems based on a transformation of the initial Markov process which includes a cost functional. The transformation of initial Markov process by cost functional has an analytic realization in terms of a Kimura-Maruyama type equation for the time evolution of states or in terms of the corresponding Feynman-Kac formula on the path space. The state evolution of the system including the limiting behavior is studied for two types of mutation-selection models.

• OSTI ID: 22251419
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 11; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EQUATIONS
MARKOV PROCESS
TRANSFORMATIONS