From Tanaka's formula to Ito's formula: The fundamental theorem of stochastic calculus

被引：3

作者：

Rajeev, B ^{[1
]}

机构：

[1] INDIAN STAT INST,CALCUTTA 700035,W BENGAL,INDIA

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 1997年 / 107卷 / 03期

关键词：

semi-martingales; Ito formula; Tanaka formula; local times;

D O I：

10.1007/BF02867261

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we give a new proof of Ito's formula in R-n starting from the one-dimensional Tanaka formula. The proof is algebraic and does not use any limiting procedure. It uses the integration by parts formula, Fubini's theorem for stochastic integrals and essential properties of local times.

引用

页码：319 / 327

页数：9

共 16 条

[1] From Tanaka's formula to Ito's formula: The fundamental theorem of stochastic calculus
B Rajeev
Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 1997, 107 : 319 - 327
[2] An extension of Ito's formula for anticipating processes
Alos, E
Nualart, D
JOURNAL OF THEORETICAL PROBABILITY, 1998, 11 (02) : 493 - 514
[3] Ito-Follmer calculus in Banach spaces I: the Ito formula*
Hirai, Yuki
ELECTRONIC JOURNAL OF PROBABILITY, 2023, 28 : 1 - 42
[4] An Ito type formula for the additive stochastic heat equation
Bellingeri, Carlo
ELECTRONIC JOURNAL OF PROBABILITY, 2020, 25
[5] A note on the Ito formula of stochastic integrals in Banach spaces
Hausenblas, Erika
RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2006, 14 (01) : 45 - 58
[6] Ito formula for an extended stochastic integral with nonanticipating kernel
Norin, NV
THEORY OF PROBABILITY AND ITS APPLICATIONS, 1995, 39 (04) : 573 - 592
[7] Ito's formula for jump processes in Lp-spaces
Gyongy, Istvan
Wu, Sizhou
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2021, 131 : 523 - 552
[8] A Meyer-Ito formula for stable processes via fractional calculus
Cano, Alejandro Santoyo
Bravo, Geronimo Uribe
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2023, 26 (2) : 619 - 650
[9] Extension and Application of Ito's Formula Under G-Framework
Zhang, Bo
Xu, Jing
Kannan, D.
STOCHASTIC ANALYSIS AND APPLICATIONS, 2010, 28 (02) : 322 - 349
[10] Ito's formula in UMD Banach spaces and regularity of solutions of the Zakai equation
Brzezniak, Z.
van Neerven, J. M. A. M.
Veraar, M. C.
Weis, L.
JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 245 (01) : 30 - 58

← 1 2 →