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

scholarly journals An Itô formula for a family of stochastic integrals and related Wong–Zakai theorems

2013 ◽  
Vol 123 (8) ◽  
pp. 3183-3200 ◽  
Author(s):  
Paolo Da Pelo ◽  
Alberto Lanconelli ◽  
Aurel I. Stan
Keyword(s):  
Stochastic Integrals ◽  
Itô Formula ◽  
Ito 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 Itō formula under the family of continuous semimartingale measures

2016 ◽  
Vol 16 (04) ◽  
pp. 1650010 ◽  
Author(s):  
Harald Oberhauser
Keyword(s):  
Continuous Dependence ◽  
Quadratic Variation ◽  
Stochastic Integrals ◽  
Itô’S Formula ◽  
Itô Formula ◽  
Ito Formula ◽  
Underlying Process ◽  
Continuous Semimartingale ◽  
The Family ◽  
Nonlinear Functionals

Dupire [16] introduced a notion of smoothness for functionals of paths and arrived at a generalization of Itō’s formula that applies to functionals with a continuous dependence on the trajectories of the underlying process. In this paper, we study nonlinear functionals that do not have such continuity. By revisiting old work of Bichteler and Karandikar we show that one can construct pathwise versions of complex functionals like the quadratic variation, stochastic integrals or Itō processes that are still regular enough such that a functional Itō-formula applies.

scholarly journals On Itô formulas for jump processes

2021 ◽  
Author(s):  
István Gyöngy ◽  
Sizhou Wu
Keyword(s):  
Jump Processes ◽  
Stochastic Pdes ◽  
Stochastic Integrals ◽  
Itô Formula ◽  
Random Measures ◽  
Ito Formula ◽  
Poisson Random Measures ◽  
Infinite Dimensional ◽  
Wiener Processes ◽  
Finite Dimensional

AbstractA well-known Itô formula for finite-dimensional processes, given in terms of stochastic integrals with respect to Wiener processes and Poisson random measures, is revisited and is revised. The revised formula, which corresponds to the classical Itô formula for semimartingales with jumps, is then used to obtain a generalisation of an important infinite-dimensional Itô formula for continuous semimartingales from Krylov (Probab Theory Relat Fields 147:583–605, 2010) to a class of $$L_p$$ L p -valued jump processes. This generalisation is motivated by applications in the theory of stochastic PDEs.

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