On Henstock-Kurzweil method to Stratonovich integral

Haifeng Yang; Tin Lam Toh

Mathematica Bohemica (2016)

  • Volume: 141, Issue: 2, page 129-142
  • ISSN: 0862-7959

Abstract

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We use the general Riemann approach to define the Stratonovich integral with respect to Brownian motion. Our new definition of Stratonovich integral encompass the classical Stratonovich integral and more importantly, satisfies the ideal Itô formula without the “tail” term, that is, f ( W t ) = f ( W 0 ) + ∫ 0 t f ' ( W s ) ∘ d W s . Further, the condition on the integrands in this paper is weaker than the classical one.

How to cite

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Yang, Haifeng, and Toh, Tin Lam. "On Henstock-Kurzweil method to Stratonovich integral." Mathematica Bohemica 141.2 (2016): 129-142. <http://eudml.org/doc/276987>.

@article{Yang2016,
abstract = {We use the general Riemann approach to define the Stratonovich integral with respect to Brownian motion. Our new definition of Stratonovich integral encompass the classical Stratonovich integral and more importantly, satisfies the ideal Itô formula without the “tail” term, that is, \[ f(W\_\{t\})= f(W\_\{0\})+\int \_\{0\}^\{t\}f^\{\prime \}(W\_\{s\})\circ \{\rm d\}W\_\{s\}. \] Further, the condition on the integrands in this paper is weaker than the classical one.},
author = {Yang, Haifeng, Toh, Tin Lam},
journal = {Mathematica Bohemica},
keywords = {Itô formula; Henstock-Kurzweil approach; Stratonovich integral},
language = {eng},
number = {2},
pages = {129-142},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On Henstock-Kurzweil method to Stratonovich integral},
url = {http://eudml.org/doc/276987},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Yang, Haifeng
AU - Toh, Tin Lam
TI - On Henstock-Kurzweil method to Stratonovich integral
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 2
SP - 129
EP - 142
AB - We use the general Riemann approach to define the Stratonovich integral with respect to Brownian motion. Our new definition of Stratonovich integral encompass the classical Stratonovich integral and more importantly, satisfies the ideal Itô formula without the “tail” term, that is, \[ f(W_{t})= f(W_{0})+\int _{0}^{t}f^{\prime }(W_{s})\circ {\rm d}W_{s}. \] Further, the condition on the integrands in this paper is weaker than the classical one.
LA - eng
KW - Itô formula; Henstock-Kurzweil approach; Stratonovich integral
UR - http://eudml.org/doc/276987
ER -

References

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