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

共 50 条

[1] On integration with respect to the q-Brownian motion
Bryc, Wlodek
STATISTICS & PROBABILITY LETTERS, 2014, 94 : 257 - 266
[2] An Introduction to (Stochastic) Calculus with Respect to Fractional Brownian Motion
Coutin, Laure
SEMINAIRE DE PROBABILITES XL, 2007, 1899 : 3 - 65
[3] Stochastic integration with respect to q Brownian motion
Donati-Martin, C
PROBABILITY THEORY AND RELATED FIELDS, 2003, 125 (01) : 77 - 95
[4] Stochastic integration with respect to q Brownian motion
C. Donati-Martin
Probability Theory and Related Fields, 2003, 125 : 77 - 95
[5] Existence and uniqueness of the entropy solution of a stochastic conservation law with a Q-Brownian motion
Funaki, Tadahisa
Gao, Yueyuan
Hilhorst, Danielle
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (09) : 5860 - 5886
[6] A dynamical version of the SYK model and the q-Brownian motion
Pluma, Miguel
Speicher, Roland
RANDOM MATRICES-THEORY AND APPLICATIONS, 2022, 11 (03)
[7] CONVERGENCE OF A FINITE VOLUME SCHEME FOR A STOCHASTIC CONSERVATION LAW INVOLVING A Q-BROWNIAN MOTION
Funaki, Tadahisa
Gao, Yueyuan
Hilhorst, Danielle
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2018, 23 (04): : 1459 - 1502
[8] Stochastic calculus with respect to free Brownian motion and analysis on Wigner space
Biane, P
Speicher, R
PROBABILITY THEORY AND RELATED FIELDS, 1998, 112 (03) : 373 - 409
[9] Stochastic calculus with respect to free Brownian motion and analysis on Wigner space
Philippe Biane
Roland Speicher
Probability Theory and Related Fields, 1998, 112 : 373 - 409
[10] Stochastic calculus for Brownian motion on a Brownian fracture
Khoshnevisan, D
Lewis, TM
ANNALS OF APPLIED PROBABILITY, 1999, 9 (03): : 629 - 667

← 1 2 3 4 5 →