The Ito Formula

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

scholarly journals Itô Formula for Free Stochastic Integrals

2002 ◽  
Vol 188 (1) ◽  
pp. 292-315 ◽  
Author(s):  
Michael Anshelevich
Keyword(s):  
Stochastic Integrals ◽  
Itô Formula ◽  
Ito Formula

A remark on the proof of Itô's formula for C2 functions of continuous semimartingales

1992 ◽  
Vol 29 (01) ◽  
pp. 216-221
Author(s):  
Wilfrid S. Kendall
Keyword(s):  
Fundamental Theorem ◽  
Short Note ◽  
Stochastic Calculus ◽  
Itô’S Formula ◽  
Itô Formula ◽  
Ito Formula ◽  
Multivariate Case ◽  
Itô's Formula ◽  
Ito’S Formula ◽  
Ito's Formula

The Itô formula is the fundamental theorem of stochastic calculus. This short note presents a new proof of Itô's formula for the case of continuous semimartingales. The new proof is more geometric than previous approaches, and has the particular advantage of generalizing immediately to the multivariate case without extra notational complexity.

scholarly journals SUPERSYMMETRY AND BROWNIAN MOTION ON SUPERMANIFOLDS

2003 ◽  
Vol 06 (supp01) ◽  
pp. 83-102 ◽  
Author(s):  
ALICE ROGERS
Keyword(s):  
Quantum Mechanics ◽  
Brownian Motion ◽  
Morse Theory ◽  
Index Theorem ◽  
Supersymmetric Quantum Mechanics ◽  
Supersymmetric Model ◽  
Itô Formula ◽  
Ito Formula ◽  
And Brownian Motion

An anticommuting analogue of Brownian motion, corresponding to fermionic quantum mechanics, is developed, and combined with classical Brownian motion to give a generalised Feynman-Kac-Itô formula for paths in geometric supermanifolds. This formula is applied to give a rigorous version of the proofs of the Atiyah-Singer index theorem based on supersymmetric quantum mechanics. After a discussion of the BFV approach to the quantization of theories with symmetry, it is shown how the quantization of the topological particle leads to the supersymmetric model introduced by Witten in his study of Morse theory.

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