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Non-Linear Extensions of Classical and Quantum Stochastic Calculus and Essentially Infinite Dimensional Analysis

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Probability Towards 2000

Part of the book series: Lecture Notes in Statistics ((LNS,volume 128))

Abstract

It is likely (at least for its proponent) that quantum probability, or more generally algebraic probability shall play for probability a role analogous to that played by algebraic geometry for geometry: many will complain against a loss of immediate intuition, but this is compensated for by an increase in power, the latter being measured by the capacity of solving old problems, not only inside probability theory, or at least of bringing non-trivial contributions to their advancement. The present, reasonably satisfactory, balance between developement of new techniques and problems effectively solved by these new tools should be preserved in order to prevent implosion into a self-substaining circle of problems and the main route to achieve this goal is the same as for classical probability, namely to keep a strong contact with advanced mathematical developement on one side and with real statistical data, wherever they come from, on the other.

Dedicated to K.R. Parthasarathy on the occasion of his 60th birthday

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Author information

Authors and Affiliations

  1. Graduate School of Polymathematics, Nagoya University, Nagoya, 464-01, Japan

    Luigi Accardi

  2. Centro Matematico Vito Volterra, Università di Roma, Roma, 00133, Italy

    Luigi Accardi

  3. Dipartimento di Matematica, Università di Bari, Bari, 70125, Italy

    Yun-Gang Lu

  4. Steklov Mathematical Institute, Russian Academy of Sciences, Vavilov St. 42, 117966, Moscow, Russia

    Igor Volovich

Authors
  1. Luigi Accardi
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  2. Yun-Gang Lu
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  3. Igor Volovich
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Editor information

Editors and Affiliations

  1. Centro Vito Volterra, Universita degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica, 00133, Roma, Italy

    L. Accardi

  2. Department of Statistics, Columbia University, 2990 Broadway Mail Code 4403, 10027, New York, NY, USA

    C. C. Heyde

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Accardi, L., Lu, YG., Volovich, I. (1998). Non-Linear Extensions of Classical and Quantum Stochastic Calculus and Essentially Infinite Dimensional Analysis. In: Accardi, L., Heyde, C.C. (eds) Probability Towards 2000. Lecture Notes in Statistics, vol 128. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2224-8_1

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  • DOI: https://doi.org/10.1007/978-1-4612-2224-8_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98458-2

  • Online ISBN: 978-1-4612-2224-8

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