The Stratonovich Interpretation of Quantum Stochastic Approximations

John Gough*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (SciVal)


The Stratonovich version of non-commutative stochastic calculus is introduced and shown to be equivalent to the Itô version developed by Hudson and Parthasarathy [1]. The conversion from Stratonovich to Itô version is shown to be implemented by a stochastic form of Wick's theorem: that is, involving the normal ordering of time-dependent noise fields. It is shown for a model of a quantum mechanical system coupled to a Bosonic field in a Gaussian state that under suitable scaling limits, in particular the weak coupling limit (for linear interactions) and low density limit (for scattering interactions), the limit form of the dynamical equation of motion is most naturally described as a quantum stochastic differential equation of Stratonovich form. We then convert the limit dynamical equations from Stratonovich to Itô form. Thermal Stratonovich noises are also presented.

Original languageEnglish
Pages (from-to)213-233
Number of pages21
JournalPotential Analysis
Issue number3
Publication statusPublished - 1999
Externally publishedYes


  • Quantum noise
  • Quantum probability
  • Stochastic analysis
  • Stratonovich interpretation


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