Abstract
A stochastic calculus based on integral kernels is developed for the Wiener process. The application of integral kernels to other types of noise is indicated.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D.B. Applebaum, R.L. Hudson: "Fermion Ito's formula and stochastic evolutions", Comm. Math. Phys. 96 (1984) 473–496.
C. Barnett, R.F. Streater, I.F. Wilde: "The Ito-Clifford integral", Journ. Func. Anal. 48(1982)172–212.
Cockroft, Hudson: "Quantum mechanical Wiener process", Journ. Multiv. Anal. 7(1977)107–124.
A. Frigerio: "Quantum Poisson processes: Physical motivations and applications", this volume.
A. Frigerio, H. Maassen: "Quantum Poisson processes and dilations of dynamical semigroups", preprint, Nijmegen.
R.L. Hudson, K.R. Parthasarathy: "Quantum Ito's formula and stochastic evolutions", Comm. Math. Phys. 93(1984)301–323.
B. Kümmerer: "Markov dilations and non-commutative Poisson processes", preprint, Tubingen.
J.M. Lindsay, H. Maassen: "The stochastic calculus of Bose noise" preprint, Nijmegen.
P.A. Meyer: "Eléments de probabilités quantiques", Exposés I à V, Inst. de Math., Université Louis Pasteur, F-67084 Strasbourg Cedex.
K.R. Parthasarathy, K.B. Sinha: "Boson-fermion relations in several dimensions" Pramana Journ. Phys. 27(1986) 105–116.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Lindsay, M., Maassen, H. (1988). An integral kernel approach to noise. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications III. Lecture Notes in Mathematics, vol 1303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078063
Download citation
DOI: https://doi.org/10.1007/BFb0078063
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18919-0
Online ISBN: 978-3-540-38846-3
eBook Packages: Springer Book Archive