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Stochastic Calculus in Fock Space

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1538)

Abstract

In this chapter, we reach the main topic of these notes, non-commutative stochastic calculus for adapted families of operators on Fock space, with respect to the basic operator martingales. This calculus is a direct generalization of the classical Ito integration of adapted stochastic processes w.r.t. Brownian motion, or other martingales. Its physical motivation is quantum mechanical evolution in the presence of a “quantum noise”. Stochastic calculus has also been developed for fermions in a series of papers by Barnett, Streater and Wilde [BSW], and in abstract versions by Accardi, Fagnola, Quaegebeur.

Keywords

  • Stochastic Differential Equation
  • Stochastic Integral
  • Stochastic Calculus
  • Rigorous Result
  • Initial Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1993 Springer-Verlag Berlin Heidelberg

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Meyer, PA. (1993). Stochastic Calculus in Fock Space. In: Quantum Probability for Probabilists. Lecture Notes in Mathematics, vol 1538. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21558-6_6

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  • DOI: https://doi.org/10.1007/978-3-662-21558-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56476-8

  • Online ISBN: 978-3-662-21558-6

  • eBook Packages: Springer Book Archive