A Lévy-Ciesielski Expansion for Quantum Brownian Motion and the Construction of Quantum Brownian Bridges

DOI10.1515/JAA.2007.275zbMath1201.81080OpenAlexW2109664520MaRDI QIDQ5454871

David Applebaum

Publication date: 3 April 2008

Published in: Journal of Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jaa.2007.275

zbMATH Keywords

Haar systemFock spacequantum Brownian motionSchauder systemexponential vectordaggered spaceLevy-Ciesielski expansionprobabilistic Hilbertian structurequantum Brownian bridgestochastic Hilbertian structure

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Fractional processes, including fractional Brownian motion (60G22) Quantum stochastic calculus (81S25) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Stochastic analysis (60H99)

Cites Work

• An example of a generalized Brownian motion
• Quantum Ito's formula and stochastic evolutions
• A non-commutative martingale representation theorem for non-Fock quantum Brownian motion
• The strong Markov property for fermion Brownian motion
• Quantum mechanical Wiener processes
• Stochastic calculus with respect to free Brownian motion and analysis on Wigner space
• Noncommutative Brownian motion in monotone Fock space
• A quantum-mechanical central limit theorem
• Quantum stochastic processes

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