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On the almost sure running maxima of solutions of affine stochastic functional differential equations

Appleby, John A.D. and Mao, Xuerong and Wu, H. (2010) On the almost sure running maxima of solutions of affine stochastic functional differential equations. SIAM Journal on Mathematical Analysis, 42 (2). pp. 646-678. ISSN 0036-1410

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Abstract

This paper studies the large fluctuations of solutions of scalar and finite-dimensional affine stochastic functional differential equations with finite memory as well as related nonlinear equations. We find conditions under which the exact almost sure growth rate of the running maximum of each component of the system can be determined, both for affine and nonlinear equations. The proofs exploit the fact that an exponentially decaying fundamental solution of the underlying deterministic equation is sufficient to ensure that the solution of the affine equation converges to a stationary Gaussian process.

Item type: Article
ID code: 29101
Keywords: stochastic functional differential equation , differential resolvent, stationary process , gaussian process, finite delay , asymptotic estimation , running maxima, Probabilities. Mathematical statistics, Computational Mathematics, Analysis, Applied Mathematics
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Pure Administrator
Date Deposited: 22 Mar 2011 12:12
Last modified: 24 Jul 2015 09:09
URI: http://strathprints.strath.ac.uk/id/eprint/29101

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