International Journal of Theoretical Physics

, Volume 34, Issue 8, pp 1481–1486 | Cite as

Higher order Ito product formula and generators of evolutions and flows

  • P. Beazley Cohen
  • T. M. W. Eyre
  • R. L. Hudson
Article

Abstract

A simple combinatorial formula is found for the product of two iterated quantum stochastic integrals, and used to find conditions that such an integral represent a unitary-valued or*-algebra homomorphism-valued process.

Keywords

Field Theory Elementary Particle Quantum Field Theory Product Formula Stochastic Integral 

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References

  1. Evans, M. P. (1989). Existence of quantum diffusions,Probability Theory and Related Fields,81, 473–483.Google Scholar
  2. Hudson, R. L. (1990). Quantum stochastic flows, inProbability Theory and Mathematical Statistics, Vol. 1, B. Grigelioniset al., eds., VSP Utrecht, pp. 512–525.Google Scholar
  3. Hudson, R. L., and Parthasarathy, K. R. (1984). Quantum Ito's formula and stochastic evolutions,Communications in Mathematical Physics,93, 301–323.Google Scholar
  4. Hudson, R. L., and Parthasarathy, K. R. (1993). Casimir chaos map for U(N).Tatra Mountains Mathematical Publications,3, 1–9.Google Scholar
  5. Parthasarathy, K. R. (1992).An Introduction to Quantum Stochastic Calculus, Birkhäuser, Basle.Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • P. Beazley Cohen
    • 1
  • T. M. W. Eyre
    • 2
  • R. L. Hudson
    • 2
  1. 1.URA 747 CNRS, Collège de FranceParisFrance
  2. 2.Mathematics DepartmentUniversity of NottinghamNottinghamUK

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