Quantum Stochastic Integral Representations on Interacting Fock Space

Yuanbao Kang () and Caishi Wang ()
Additional contact information
Yuanbao Kang: Northwest Normal University
Caishi Wang: Northwest Normal University

Journal of Theoretical Probability, 2015, vol. 28, issue 3, 1007-1027

Abstract: Abstract A quantum stochastic integration theory on interacting Fock space (IFS) has been established in Crismale (Commun Stoch Anal 1(2):321–341, 2007). In this paper, we firstly put forward a family of left–right conditional expectations $$E_{t}$$ E t , for $$t\in R_{+}$$ t ∈ R + , on the von Neumann algebra $$\mathcal {V}$$ V generated by the creation, annihilation and gauge operators acting on IFS over $${L}^{2}(R_{+})$$ L 2 ( R + ) . Next, we develop a generalized quantum stochastic integral. Finally, we prove that any process $$\Xi \in (\mathcal {V}_{t})_{t\in R_{+}}$$ Ξ ∈ ( V t ) t ∈ R + admits a quantum stochastic integral representation.

Keywords: Interacting Fock spaces (IFS); Quantum stochastic integral; Quantum stochastic process; Quantum stochastic integral representation.; 81S25; 46L53 (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-013-0537-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:28:y:2015:i:3:d:10.1007_s10959-013-0537-5

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-013-0537-5

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().