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
相关论文
共 50 条
  • [41] Stochastic Calculus with Respect to Gaussian Processes
    Joachim Lebovits
    Potential Analysis, 2019, 50 : 1 - 42
  • [42] Stochastic calculus with respect to Gaussian processes
    Alòs, E
    Mazet, O
    Nualart, D
    ANNALS OF PROBABILITY, 2001, 29 (02): : 766 - 801
  • [43] Stochastic Thermodynamics of Brownian Motion
    Nicolis, Gregoire
    De Decker, Yannick
    ENTROPY, 2017, 19 (09):
  • [44] GENERALIZED BROWNIAN-MOTION, POINT-PROCESSES AND STOCHASTIC CALCULUS FOR RANDOM-FIELDS
    FICHTNER, KH
    WINKLER, G
    MATHEMATISCHE NACHRICHTEN, 1993, 161 : 291 - 307
  • [45] G-expectation, G-Brownian motion and related Stochastic calculus of ito type
    Peng, Shige
    Stochastic Analysis and Applications, 2007, 2 : 541 - 567
  • [46] Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
    Pei, Bin
    Xu, Yong
    Wu, Jiang-Lun
    APPLIED MATHEMATICS LETTERS, 2020, 100
  • [47] Besov Regularity of Stochastic Integrals with Respect to the Fractional Brownian Motion with Parameter H > 1/2
    David Nualart
    Youssef Ouknine
    Journal of Theoretical Probability, 2003, 16 : 451 - 470
  • [48] Stability with respect to a part of the variables of stochastic nonlinear systems driven by G-Brownian motion
    Caraballo, Tomas
    Ezzine, Faten
    Hammami, Mohamed Ali
    INTERNATIONAL JOURNAL OF CONTROL, 2023, 96 (07) : 1797 - 1809
  • [49] Integration with Respect to the Hermitian Fractional Brownian Motion
    Deya, Aurelien
    JOURNAL OF THEORETICAL PROBABILITY, 2020, 33 (01) : 295 - 318
  • [50] On the Wiener integral with respect to the fractional Brownian motion
    Tudor, C
    BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2002, 8 (01): : 97 - 106
12345