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One remark to the Itô formula. / Ибрагимов, Ильдар Абдуллович; Смородина, Наталия Васильевна; Фаддеев, Михаил Михайлович.

In: Theory of Probability and its Applications, Vol. 69, No. 2, 01.08.2024, p. 227-242.

Research output: Contribution to journal › Article › peer-review

Harvard

Ибрагимов, ИА, Смородина, НВ & Фаддеев, ММ 2024, 'One remark to the Itô formula', Theory of Probability and its Applications, vol. 69, no. 2, pp. 227-242. https://doi.org/10.1137/s0040585x97t99188x

APA

Ибрагимов, И. А., Смородина, Н. В., & Фаддеев, М. М. (2024). One remark to the Itô formula. Theory of Probability and its Applications, 69(2), 227-242. https://doi.org/10.1137/s0040585x97t99188x

Vancouver

Ибрагимов ИА, Смородина НВ, Фаддеев ММ. One remark to the Itô formula. Theory of Probability and its Applications. 2024 Aug 1;69(2):227-242. https://doi.org/10.1137/s0040585x97t99188x

Author

Ибрагимов, Ильдар Абдуллович ; Смородина, Наталия Васильевна ; Фаддеев, Михаил Михайлович. / One remark to the Itô formula. In: Theory of Probability and its Applications. 2024 ; Vol. 69, No. 2. pp. 227-242.

BibTeX

@article{5fcd47dbcf674131bbd5c90c83898e96,
title = "One remark to the It{\^o} formula",
abstract = "In the classical It{\^o} formula, we propose replacing the second derivative (understood in the usual sense) by the second derivative in the sense of differentiation of distributions. In particular, we show that this can be done if the first derivative lies in the class L2,loc (R). Earlier, F{\"o}llmer, Protter, and Shiryayev [Bernoulli, 1 (1995), pp. 149–169] obtained a different form of the last term in the It{\^o} formula under the same conditions.",
keywords = "It{\^o} formula, distribution, local time, random process",
author = "Ибрагимов, {Ильдар Абдуллович} and Смородина, {Наталия Васильевна} and Фаддеев, {Михаил Михайлович}",
year = "2024",
month = aug,
day = "1",
doi = "10.1137/s0040585x97t99188x",
language = "English",
volume = "69",
pages = "227--242",
journal = "Theory of Probability and its Applications",
issn = "0040-585X",
publisher = "Society for Industrial and Applied Mathematics",
number = "2",

}

RIS

TY - JOUR

T1 - One remark to the Itô formula

AU - Ибрагимов, Ильдар Абдуллович

AU - Смородина, Наталия Васильевна

AU - Фаддеев, Михаил Михайлович

PY - 2024/8/1

Y1 - 2024/8/1

N2 - In the classical Itô formula, we propose replacing the second derivative (understood in the usual sense) by the second derivative in the sense of differentiation of distributions. In particular, we show that this can be done if the first derivative lies in the class L2,loc (R). Earlier, Föllmer, Protter, and Shiryayev [Bernoulli, 1 (1995), pp. 149–169] obtained a different form of the last term in the Itô formula under the same conditions.

AB - In the classical Itô formula, we propose replacing the second derivative (understood in the usual sense) by the second derivative in the sense of differentiation of distributions. In particular, we show that this can be done if the first derivative lies in the class L2,loc (R). Earlier, Föllmer, Protter, and Shiryayev [Bernoulli, 1 (1995), pp. 149–169] obtained a different form of the last term in the Itô formula under the same conditions.

KW - Itô formula

KW - distribution

KW - local time

KW - random process

UR - https://www.mendeley.com/catalogue/51040f67-7051-3376-9db6-2ab2d692fe97/

U2 - 10.1137/s0040585x97t99188x

DO - 10.1137/s0040585x97t99188x

M3 - Article

VL - 69

SP - 227

EP - 242

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 2

ER -

ID: 127711341