Fubini theorem for anticipating stochastic integrals in Hilbert space

1993 ◽  
Vol 27 (3) ◽  
pp. 313-327 ◽  
Author(s):  
Jorge A. Le�n
Keyword(s):  
Hilbert Space ◽  
Fubini Theorem ◽  
Stochastic Integrals

Stochastic Fubini Theorem for Semimartingales in Hilbert Space

1990 ◽  
Vol 42 (5) ◽  
pp. 890-901 ◽  
Author(s):  
Jorge A. León
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Measure Space ◽  
Sufficient Conditions ◽  
Linear Operators ◽  
Fubini Theorem ◽  
Stochastic Integrals ◽  
Bounded Linear ◽  
Image Position ◽  
Stochastic Fubini Theorem

In this paper we will study the Fubini theorem for stochastic integrals with respect to semimartingales in Hilbert space.Let (Ω, , P) he a probability space, (X, , μ) a measure space, H and G two Hilbert spaces, L(H, G) the space of bounded linear operators from H into G, Z an H-valued semimartingale relative to a given filtration, and φ: X × R+ × Ω → L(H, G) a function such that for each t ∈ R+ the iterated integrals are well-defined (the integrals with respect to μ are Bochner integrals). It is often necessary to have sufficient conditions for the process Y1 to be a version of the process Y2 (e.g. [1], proof of Theorem 2.11).

scholarly journals A Fubini theorem for iterated stochastic integrals

1978 ◽  
Vol 84 (1) ◽  
pp. 159-161 ◽  
Author(s):  
Marc A. Berger ◽  
Victor J. Mizel
Keyword(s):  
Fubini Theorem ◽  
Stochastic Integrals

Quasi-free stochastic integral representation theorems over the CCR

1988 ◽  
Vol 104 (2) ◽  
pp. 383-398 ◽  
Author(s):  
Ivan F. Wilde
Keyword(s):  
Hilbert Space ◽  
Integral Representation ◽  
Stochastic Integral ◽  
Stochastic Integrals ◽  
Representation Theorems ◽  
Martingale Representation ◽  
Stochastic Integral Representation ◽  
Vector Valued ◽  
General Vector

AbstractIt is shown that each vector in the Hilbert space of certain quasi-free representations of the CCR can be written uniquely in terms of quantum stochastic integrals. As a consequence, we obtain general vector-valued and operator-valued boson quantum martingale representation theorems.

scholarly journals Stochastic Integrals Based on Martingales Taking Values in Hilbert Space

1970 ◽  
Vol 38 ◽  
pp. 41-52 ◽  
Author(s):  
Hiroshi Kunita
Keyword(s):  
Hilbert Space ◽  
Probability Space ◽  
Separable Hilbert Space ◽  
Linear Operators ◽  
Inner Product ◽  
Stochastic Integrals

Let H be a separable Hilbert space with inner product (,) and norm ║ ║. We denote by K the set of all linear operators on H. Let be a probability space and suppose we are given a family of σ-fields t≥O such that for O ≤ s ≤ t and .

scholarly journals Quantum stochastic integrals as belated integrals

1992 ◽  
Vol 34 (2) ◽  
pp. 165-173
Author(s):  
Chris Barnett ◽  
J. M. Lindsay ◽  
Ivan F. Wilde
Keyword(s):  
Hilbert Space ◽  
Brownian Motion ◽  
Stochastic Integral ◽  
Stochastic Integrals ◽  
Itô Integral ◽  
Ito Integral ◽  
Finite Sum ◽  
Vector Valued ◽  
Quantum Stochastic Integral

Quantum stochastic integrals have been constructed in various contexts [2, 3, 4, 5, 9] by adapting the construction of the classical L2-Itô-integral with respect to Brownian motion. Thus, the integral is first defined for simple integrands as a finite sum, then one establishes certain isometry relations or suitable bounds to allow the extension, by continuity, to more general integrands. The integrator is typically operator-valued, the integrand is vector-valued or operator-valued and the quantum stochastic integral is then given as a vector in a Hilbert space, or as an operator on the Hilbert space determined by its action on suitable vectors.

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