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The operators of stochastic calculus.
- Source :
-
Random Operators & Stochastic Equations . Jun2024, Vol. 32 Issue 2, p185-205. 21p. - Publication Year :
- 2024
-
Abstract
- We study a family of representations of the canonical commutation relations (CCR)-algebra, which we refer to as "admissible," with an infinite number of degrees of freedom. We establish a direct correlation between each admissible representation and a corresponding Gaussian stochastic calculus. Moreover, we derive the operators of Malliavin's calculus of variation using an algebraic approach, which differs from the conventional methods. The Fock-vacuum representation leads to a maximal symmetric pair. This duality perspective offers the added advantage of resolving issues related to unbounded operators and dense domains much more easily than with alternative approaches. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MALLIAVIN calculus
*CALCULUS of variations
*CALCULUS
*DEGREES of freedom
Subjects
Details
- Language :
- English
- ISSN :
- 09266364
- Volume :
- 32
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Random Operators & Stochastic Equations
- Publication Type :
- Academic Journal
- Accession number :
- 177519662
- Full Text :
- https://doi.org/10.1515/rose-2024-2007