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

John A.D. Appleby, Xuerong Mao, H. Wu

Research output: Contribution to journalArticle

8 Citations (Scopus)

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.
LanguageEnglish
Pages646-678
Number of pages33
JournalSIAM Journal on Mathematical Analysis
Volume42
Issue number2
Early online date31 Mar 2010
DOIs
Publication statusPublished - 2010

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Stochastic Functional Differential Equations
Nonlinear equations
Differential equations
Nonlinear Equations
Stationary Gaussian Process
Fundamental Solution
Data storage equipment
Scalar
Fluctuations
Sufficient
Converge

Keywords

  • stochastic functional differential equation
  • differential resolvent
  • stationary process
  • gaussian process
  • finite delay
  • asymptotic estimation
  • running maxima

Cite this

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On the almost sure running maxima of solutions of affine stochastic functional differential equations. / Appleby, John A.D.; Mao, Xuerong; Wu, H.

In: SIAM Journal on Mathematical Analysis, Vol. 42, No. 2, 2010, p. 646-678.

Research output: Contribution to journalArticle

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AU - Mao, Xuerong

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KW - stochastic functional differential equation

KW - differential resolvent

KW - stationary process

KW - gaussian process

KW - finite delay

KW - asymptotic estimation

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