HENSTOCK'S VERSION OF ITO'S FORMULA

被引:0
|
作者
Toh, Tin Lam [1 ]
Chew, Than Seng [2 ]
机构
[1] Nanyang Technol Univ, Natl Inst Educ, 1 Nanyang Walk, Singapore 637616, Singapore
[2] Natl Univ Singapore, Singapore 117543, Singapore
关键词
Ito's formula; Henstock's stochastic integral; generalized Riemann approach;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Ito's Formula is the stochastic analogue of the change of variable formula for deterministic integrals. It is a useful tool in dealing with stochastic integration. In this paper, using Henstock's approach, we derive two versions of Ito's Formula. Henstock's or generalized Riemann approach has been successful in giving an alternative definition of stochastic integral, which is more explicit, intuitive and less measure theoretic. Henstock's approach provides a simpler and more direct proof of Ito's Formula, although we do not claim that it is a generalization of the classical results.
引用
收藏
页码:375 / 390
页数:16
相关论文
共 50 条
  • [1] Backwards Ito-Henstock's version of Ito's formula
    Rulete, Ricky F.
    Labendia, Mhelmar A.
    [J]. ANNALS OF FUNCTIONAL ANALYSIS, 2020, 11 (01) : 208 - 225
  • [2] Backwards Itô–Henstock’s version of Itô’s formula
    Ricky F. Rulete
    Mhelmar A. Labendia
    [J]. Annals of Functional Analysis, 2020, 11 : 208 - 225
  • [3] ITO-HENSTOCK INTEGRAL AND ITO'S FORMULA FOR THE OPERATOR-VALUED STOCHASTIC PROCESS
    Labendia, Mhelmar A.
    Teng, Timothy Robin Y.
    de Lara-Tuprio, Elvira P.
    [J]. MATHEMATICA BOHEMICA, 2018, 143 (02): : 135 - 160
  • [4] A Q-fractional version of Ito's formula
    Grecksch, Wilfried
    Roth, Christian
    [J]. STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2011, 56 (02): : 369 - 380
  • [5] A proof of ito's formula using a discrete ito's formula
    Fujita, Takahiko
    Kawanishi, Yasuhiro
    [J]. STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2008, 45 (01) : 125 - 134
  • [6] Henstock's multiple Wiener integral and Henstock's version of Hu-Meyer theorem
    Toh, TL
    Chew, TS
    [J]. MATHEMATICAL AND COMPUTER MODELLING, 2005, 42 (1-2) : 139 - 149
  • [7] On Ito's formula of Follmer and Protter
    Eisenbaum, N
    [J]. SEMINAIRE DE PROBABILITES XXXV, 2001, 1755 : 390 - 395
  • [8] On Ito-Kurzweil-Henstock integral and integration-by-part formula
    Tin-Lam T.
    Tuan-Seng C.
    [J]. Czechoslovak Mathematical Journal, 2005, 55 (3) : 653 - 663
  • [9] On Ito-Kurzweil-Henstock integral and integration-by-part formula
    Toh, TL
    Chew, TS
    [J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 2005, 55 (03) : 653 - 663
  • [10] Quaternion version of the Itô's formula
    Zeng, Runtian
    Song, Qiankun
    Sun, Shuning
    [J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2024, 222 : 242 - 251