Itô's stochastic calculus and Heisenberg commutation relations

DOI10.1016/j.spa.2010.01.016zbMath1194.60035OpenAlexW2019500627MaRDI QIDQ972812

Philippe Biane

Publication date: 21 May 2010

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2010.01.016

zbMATH Keywords

diffusion processesstochastic integralsHeisenberg commutation relations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Noncommutative probability and statistics (46L53) Stochastic integrals (60H05)

Related Items (6)

A stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises under uncertain environment ⋮ Quantum stochastic processes: a case study ⋮ The open quantum Brownian motions ⋮ On the small mass limit of quantum Brownian motion with inhomogeneous damping and diffusion ⋮ An algebraic construction of quantum flows with unbounded generators ⋮ Itô formula for one-dimensional continuous-time quantum random walk

Cites Work

• Quantum Ito's formula and stochastic evolutions
• Itô's stochastic calculus: its surprising power for applications
• Derivations as square roots of Dirichlet forms
• Quantum probability for probabilists.
• Chaotic representation for finite markov chains
• Spectral Type of the Shift Transformation of Differential Processes With Stationary Increments
• On Square Integrable Martingales
• On stochastic differential equations
• Stochastic integral
• On a stochastic integral equation
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