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Estimates for the state density for ordinary differential operators with white gaussian noise potential

Published online by Cambridge University Press:  14 November 2011

V. B. Moscatelli  and
M. Thompson
V. B. Moscatelli
Affiliation:
Instituto di Mathematicà, Universita CP 113, Via Arnessano 13100, Lecce, Italia
M. Thompson
Affiliation:
Dept° de Mathemática, U.F.R.G.S. 3° andar, 425 Rua Sarmento Leite, 90.000 - Porto Alegre, Rio Grande do Sul, Brasil
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Synopsis

The present paper is concerned with developing the existence and asymptotic properties of the state density N(λ) associated with certain higher order random ordinary differential operators A of the form

where Ao has homogeneous and ergodic coefficients with respect to the σ-algebra generated by the Wiener process q(ω, x). The analysis uses the Weyl min-max principle to determine rough upper and lower bounds for N(λ).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 3-4 , 1983 , pp. 263 - 274
Copyright
Copyright © Royal Society of Edinburgh 1983

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