Adjoint equation and Lyapunov regularity for linear stochastic differential algebraic equations of index 1

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-08-05 DOI:10.1080/17442508.2013.879141

N. D. Cong, S. Siegmund, N. The

引用次数: 0

Abstract

We introduce a concept of adjoint equation and Lyapunov regularity of a stochastic differential algebraic Equation (SDAE) of index 1. The notion of adjoint SDAE is introduced in a similar way as in the deterministic differential algebraic equation case. We prove a multiplicative ergodic theorem for the adjoint SDAE and the adjoint Lyapunov spectrum. Employing the notion of adjoint equation and Lyapunov spectrum of an SDAE, we are able to define Lyapunov regularity of SDAEs. Some properties and an example of a metal oxide semiconductor field-effect transistor ring oscillator under thermal noise are discussed.

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指标1的线性随机微分代数方程的伴随方程和Lyapunov正则性

引入指标1的随机微分代数方程(SDAE)的伴随方程和Lyapunov正则性概念。伴随SDAE的概念以与确定性微分代数方程类似的方式引入。我们证明了伴随SDAE和伴随Lyapunov谱的一个乘法遍历定理。利用伴随方程和Lyapunov谱的概念，我们可以定义SDAE的Lyapunov正则性。讨论了金属氧化物半导体场效应晶体管环振荡器在热噪声作用下的一些特性，并给出了一个例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.