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Quantum stop times

Part of the Lecture Notes in Mathematics book series (LNM,volume 1396)

Abstract

The notion of stop-time can be naturally translated in a quantum probabilistic framework and this problem has been studied by several authors [1], [2], [3], [4], [5]. Recently Parthasarathy and Sinha [4] have established a factorization property of the L 2-space over the Wiener space (regarded as the Fock space over L 2(R +)) based on the notion of quantum stop time which is a quantum probabilistic analogue of the strong Markov property. In this note we prove a stronger result which has no classical analogue namely that the algebra generated by the stopped Weyl operators in the sense of [4] (i.e.the past algebra with respect to a stop time S), is the algebra of all the bounded operators on L 2 of the Wiener space.

Keywords

  • Classical Analogue
  • Factorization Property
  • Indian Statistical Institute
  • Stop Time
  • Wiener Space

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Bibliography

  1. Applebaum D. The strong Markov property for Fermion Brownian motion. J. Func. Anal. 65(1986)273–391

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Barnett C., Lyons T. Stopping noncommuting processes. Math. Proc. Camb. Phil. Soc. 99(1986)151–161

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  3. Hudson R.L. The strong Markov property for canonical Wiener processes. J. Func. Anal. 34(1979)266

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  4. Parthasarathy K.R., Sinha K. Stop times in Fock space stochastic calculus. to appear in Probability Theory and related fields.

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  5. Sauvageot J.L. First exit time: a theory of stopping times in quantum processes. in Quantum Probability III. Springer LNM N.1303,285–299

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© 1989 Springer-Verlag

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Accardi, L., Sinha, K. (1989). Quantum stop times. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications IV. Lecture Notes in Mathematics, vol 1396. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083544

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  • DOI: https://doi.org/10.1007/BFb0083544

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51613-2

  • Online ISBN: 978-3-540-46713-7

  • eBook Packages: Springer Book Archive