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 (https://doi.org/10.1137/080738404)
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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.
ORCID iDs
Appleby, John A.D., Mao, Xuerong ORCID: https://orcid.org/0000-0002-6768-9864 and Wu, H.;-
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Item type: Article ID code: 29101 Dates: DateEvent2010Published31 March 2010Published OnlineSubjects: 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: 25 Sep 2024 00:34 URI: https://strathprints.strath.ac.uk/id/eprint/29101