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
收藏
页码：1047 / 1075
页数：29
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