Abstract
We show that iterated stochastic integrals (in the Itô-sense) with respect to the Brownian bridge on R d give an explicit unitary isomorphism between the symmetric Fock space over the C d-valued square-integrable functions on the unit interval having zero mean and the space of complex valued L 2-functions on based continuous loops on R d.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
[BR] M.J. Bowick and S.G. Rajeev, The holomorphic geometry of closed bosonic string theory and Diff(S 1)/S 1, Nucl. Phys. B 293 (1987) 348–384.
[DMM] C. Dellacherie, B. Maisonneuve et P.-A. Meyer, Probabilités et Potentiel. Chapitres XVII à XXIV (Hermann, Paris 1992).
[GW] P. Gosselin and T. Wurzbacher, A stochastic approach to the Virasoro anomaly in quantization of strings in flat space, Preprint 1996.
[HLP] G. Hardy, J.E. Littlewood and G. Pólya, Inequalities (Cambridge at the University Press 1934).
[HT] W. Hackenbroch und A. Thalmaier, Stochastische Analysis (B.G. Teubner, Stuttgart 1994).
[JY] T. Jeulin et M. Yor, Inégalité de Hardy, semi-martingales, et faux-amis, Séminaire de Probabilités XIII (1977/78), LNM 721. 332–359.
[M] P.-A. Meyer, Quantum Probability for Probabilists (Springer LNM 1538, Berlin Heidelberg 1993).
[N] J. Neveu, Processus aléatoires gaussiens (Les Presses de l’Université de Montréal 1968).
[PS] A. Pressley and G. Segal, Loop groups (Oxford University Press 1986).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gosselin, P., Wurzbacher, T. (1997). An Itô type isometry for loops in Rd via the Brownian bridge. In: Azéma, J., Yor, M., Emery, M. (eds) Séminaire de Probabilités XXXI. Lecture Notes in Mathematics, vol 1655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0119307
Download citation
DOI: https://doi.org/10.1007/BFb0119307
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62634-3
Online ISBN: 978-3-540-68352-0
eBook Packages: Springer Book Archive