Lyapunov Exponents of Linear Stochastic Functional Differential Equations Part Ii: Examples and Case Studies
نویسندگان
چکیده
We give several examples and examine case studies of linear stochastic functional di erential equations. The examples fall into two broad classes: regular and singular, according to whether an underlying stochastic semi ow exists or not. In the singular case, we obtain upper and lower bounds on the maximal exponential growth rate 1 ( ) of the trajectories expressed in terms of the noise variance . Roughly speaking we show that for small , 1 ( ) behaves like 2 2 , while for large , it grows like log . In the regular case, it is shown that a discrete Oseledec spectrum exists, and upper estimates on the top exponent 1 are provided. These estimates are sharp in the sense they reduce to known estimates in the deterministic or non-delay cases.
منابع مشابه
Lyapunov Exponents of Linear Stochastic Functional-Differential Equations. II. Examples and Case Studies
We give several examples and examine case studies of linear stochastic functional differential equations. The examples fall into two broad classes: regular and singular, according to whether an underlying stochastic semi-flow exists or not. In the singular case, we obtain upper and lower bounds on the maximal exponential growth rate λ 1 σ of the trajectories expressed in terms of the noise vari...
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