Itô stochastic integral. Itô formula. Tanaka formula

2009 ◽  
pp. 193-213
Author(s):  
Dmytro Gusak ◽  
Alexander Kukush ◽  
Alexey Kulik ◽  
Yuliya Mishura ◽  
Andrey Pilipenko
Keyword(s):  
Stochastic Integral ◽  
Itô Formula ◽  
Ito Formula ◽  
Tanaka Formula

Stochastic Integrals

2019 ◽  
pp. 43-66
Author(s):  
Tomas Björk
Keyword(s):  
Wiener Process ◽  
Stochastic Integral ◽  
Stochastic Integrals ◽  
Itô Formula ◽  
Martingale Theory ◽  
Ito Formula

We introduce the Wiener process, the Itô stochastic integral, and derive the Itô formula. The connection with martingale theory is discussed, and there are several worked-out examples

scholarly journals The functional Meyer–Tanaka formula

2018 ◽  
Vol 18 (04) ◽  
pp. 1850030 ◽  
Author(s):  
Yuri F. Saporito
Keyword(s):  
Time Dependent ◽  
Itô Formula ◽  
Convergence Properties ◽  
Ito Formula ◽  
Underlying Process ◽  
Running Maximum ◽  
Functional Version ◽  
Tanaka Formula

The functional Itô formula, firstly introduced by Bruno Dupire for continuous semimartingales, might be extended in two directions: different dynamics for the underlying process and/or weaker assumptions on the regularity of the functional. In this paper, we pursue the former type by proving the functional version of the Meyer–Tanaka formula. Following the idea of the proof of the classical time-dependent Meyer–Tanaka formula, we study the mollification of functionals and its convergence properties. As an example, we study the running maximum and the max-martingales of Yor and Obłój.

On the Ito formula in a Banach Space

2000 ◽  
Vol 7 (1) ◽  
pp. 155-168
Author(s):  
B. Mamporia
Keyword(s):  
Banach Space ◽  
Continuous Function ◽  
Wiener Process ◽  
Separable Banach Space ◽  
Stochastic Integral ◽  
Covariance Operator ◽  
Itô Formula ◽  
Ito Formula ◽  
Special Construction ◽  
Frechet Derivatives

Abstract If (Wt ) t∈[ 0, 1] is a Wiener process in an arbitrary separable Banach space X, ψ : [0, 1] × X → Y is a continuous function with values in another separable Banach space, and ψ has continuous Frechet derivatives , and , then the Ito formula is obtained for ψ(t, Wt ). The method is based on the concept of covariance operator and a special construction of the Ito stochastic integral.

scholarly journals The Itô formula for a new stochastic integral

2012 ◽  
Vol 6 (4) ◽  
Author(s):  
Hui-Hsiung Kuo ◽  
Anuwat Sae-Tang ◽  
Benedykt Szozda
Keyword(s):  
Stochastic Integral ◽  
Itô Formula ◽  
Ito Formula

scholarly journals A generalization of the Itô formula

2002 ◽  
Vol 31 (8) ◽  
pp. 477-496
Author(s):  
Said Ngobi
Keyword(s):  
Sobolev Space ◽  
White Noise ◽  
Itô Formula ◽  
Ito Formula ◽  
Integrable Functions ◽  
Square Integrable Functions ◽  
White Noise Space

The classical Itô formula is generalized to some anticipating processes. The processes we consider are in a Sobolev space which is a subset of the space of square integrable functions over a white noise space. The proof of the result uses white noise techniques.

An Ito formula for domain-valued processes driven by stochastic flows

2002 ◽  
Vol 124 (1) ◽  
pp. 73-99 ◽  
Author(s):  
Kimberly Kinateder ◽  
Patrick McDonald
Keyword(s):  
Stochastic Flows ◽  
Itô Formula ◽  
Ito Formula

The Ito Formula

1983 ◽  
pp. 85-103
Author(s):  
K. L. Chung ◽  
R. J. Williams
Keyword(s):  
Itô Formula ◽  
Ito Formula
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