Self-regulating processes

被引：9

作者：

Barriere, Olivier ^{[1
]}

Echelard, Antoine ^{[2
,3
]}

Vehel, Jacques Levy ^{[2
,3
]}

机构：

[1] Irccyn, Fractales Team, Nantes, France

[2] Ecole Cent Paris, Regular Team, Inria, Paris, France

[3] Ecole Cent Paris, MAS Lab, Paris, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2012年 / 17卷

关键词：

Holder regularity; Weierstrass function; multifractional Brownian motion; self-regulating processes; BROWNIAN MOTIONS;

D O I：

10.1214/EJP.v17-2010

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We construct functions and stochastic processes for which a functional relation holds between amplitude and local regularity, as measured by the pointwise or local Holder exponent. We consider in particular functions and processes built by extending Weierstrass function, multifractional Brownian motion and the Levy construction of Brownian motion. Such processes have recently proved to be relevant models in various applications. The aim of this work is to provide a theoretical background to these studies and to provide a first step in the development of a theory for such self-regulating processes.

引用

页码：1 / 30

页数：30

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