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Noncommutative stochastic processes with independent and stationary increments satisfy quantum stochastic differential equations
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  • Published: December 1990

Noncommutative stochastic processes with independent and stationary increments satisfy quantum stochastic differential equations

  • Michael Schürmann1 

Probability Theory and Related Fields volume 84, pages 473–490 (1990)Cite this article

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  • 11 Citations

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Summary

The notion of a unitary noncommutative stochastic process with independent and stationary increments is introduced, and it is proved that such a process, under a continuity assumption, can be embedded into the solution of a quantum stochastic differential equation in the sense of Hudson and Parthasarathy [8].

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, D-6900, Heidelberg 1, Federal Republic of Germany

    Michael Schürmann

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  1. Michael Schürmann
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Additional information

This work was supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 123, ‘Stochastische Mathematische Modelle’

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Schürmann, M. Noncommutative stochastic processes with independent and stationary increments satisfy quantum stochastic differential equations. Probab. Th. Rel. Fields 84, 473–490 (1990). https://doi.org/10.1007/BF01198315

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  • Received: 23 April 1988

  • Revised: 11 August 1989

  • Issue Date: December 1990

  • DOI: https://doi.org/10.1007/BF01198315

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Keywords

  • Differential Equation
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Stochastic Differential Equation
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