ON THE ALMOST SURE RUNNING MAXIMA OF SOLUTIONS OF AFFINE STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

被引：9
作者：
Appleby, John A. D. [1 ]
Mao, Xuerong [2 ]
Wu, Huizhong [1 ]
机构：
[1] Dublin City Univ, Edgeworth Ctr Financial Math, Sch Math Sci, Dublin 9, Ireland
[2] Univ Strathclyde, Dept Stat & Modelling Sci, Glasgow G1 1XT, Lanark, Scotland
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2010年 / 42卷 / 02期
基金：
爱尔兰科学基金会;
关键词：
stochastic functional differential equation; Gaussian process; stationary process; differential resolvent; running maxima; almost sure asymptotic estimation; finite delay; GAUSSIAN-PROCESSES; ITERATED LOGARITHM; FINANCIAL-MARKETS; VOLTERRA-EQUATIONS; DELAY EQUATIONS; ARMA PROCESSES; STABILITY; MEMORY; INCREMENTS; THEOREMS;
D O I：
10.1137/080738404
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：646 / 678
页数：33
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