On stochastic calculus with respect to q-Brownian motion

被引：4

作者：

Deya, Aurelien ^{[1
]}

Schott, Rene ^{[1
]}

机构：

[1] Univ Lorraine, Inst Elie Carton, BP 239, F-54506 Vandoeuvre Les Nancy, France

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2018年 / 274卷 / 04期

关键词：

Non-commutative stochastic calculus; q-Brownian motion; Rough paths theory; ROUGH-PATHS;

D O I：

10.1016/j.jfa.2017.08.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Following the approach and the terminology introduced in Deya and Schott (2013) [6], we construct a product Levy area above the q-Brownian motion (for q is an element of [0,1)) and use this object to study differential equations driven by the process. We also provide a detailed comparison between the resulting "rough" integral and the stochastic "Ito" integral exhibited by Donati-Martin (2003) [7]. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：1047 / 1075

页数：29

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