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On the Ito formula in a Banach Space
-
B. Mamporia
Published/Copyright:
February 18, 2010
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.
Key words and phrases.: Wiener processes and stochastic integrals in Banach space; Ito formula; Gaussian measures and Gaussian covariances in Banach space
Received: 1998-05-01
Published Online: 2010-02-18
Published in Print: 2000-March
© Heldermann Verlag
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Articles in the same Issue
- On Fourier Coefficients of Functions of Generalized Wiener Class
- Asymptotic Distribution of Eigenelements of the Basic Two-Dimensional Boundary-Contact Problems of Oscillation in Classical and Couple-Stress Theories of Elasticity
- New Proofs of Two-Weight Norm Inequalities for the Maximal Operator
- Convergent Rearrangements of Series of Vector-Valued Functions
- On the Convergence and Summability of N-Dimensional Fourier Series with Respect to the Walsh–Paley Systems in the Spaces LP([0, 1]N), p ∈ [1, + ∞]
- A Direct Boundary Integral Method for a Mobility Problem
- Unconditional Convergence of Random Series and the Geometry of Banach Spaces
- Quasi-Linearisation Methods for a Non-Linear Heat Equation with Functional Dependence
- On State Space Representations of AR-Models
- On a Nonlocal Boundary Value Problem for Second Order Nonlinear Singular Differential Equations
- On the Ito formula in a Banach Space
- On the Rearranged Block-Orthonormal Systems
- Classification of Singularities at Infinity of Polynomials of Degree 4 in Two Variables
- Qualitative Investigation of Two-Dimensional Chua's System
