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Stochastic integral representation theorem for quantum semimartingales

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
201
Issue
1
Identifiers
DOI: 10.1016/s0022-1236(02)00027-7
Keywords
  • Boson Fock Space
  • Quantum Stochastic Process
  • Quantum Stochastic Integral
  • Quantum Itô Formula
  • Quantum Martingale
  • Quantum Semimartingale
Disciplines
  • Mathematics
  • Physics

Abstract

Abstract The quantum stochastic integral of Itô type formulated by Hudson and Parthasarathy is extended to a wider class of adapted quantum stochastic processes on Boson Fock space. An Itô formula is established and a quantum stochastic integral representation theorem is proved for a class of unbounded semimartingales which includes polynomials and (Wick) exponentials of the basic martingales in quantum stochastic calculus.

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