On characterizing quantum stochastic evolutions

DOI10.1017/S0305004100067372zbMath0644.46046OpenAlexW2153583266MaRDI QIDQ3786956

J. Martin Lindsay, Robin L. Hudson

Publication date: 1987

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100067372

zbMATH Keywords

quantum diffusionsnorm continuous quantum stochastic evolutionsQuantum stochastic calculus in Boson Fock spacequantum stochastic differential equations with bounded coefficients

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Stochastic mechanics (including stochastic electrodynamics) (81P20)

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Stochastic cocyles over \(\mathbb{Z}_ 2\)-graded \(^*\)-algebras, Towards characterizing quantum stochastic fermionic evolutions, Module white noise calculus, On quantum stochastic differential equations, Stochastic integral representation theorem for quantum semimartingales., A quantum stochastic Lie-Trotter product formula, Characterization of unitary processes with independent and stationary increments, Noncommutative stochastic processes with independent and stationary increments satisfy quantum stochastic differential equations, Unitary processes with independent increments and representations of Hilbert tensor algebras, Markovian cocycles on operator algebras adapted to a Fock filtration, WHITE NOISE HEISENBERG EVOLUTION AND EVANS–HUDSON FLOWS, Flows of Quantum Noise

Cites Work

• Stochastic dilations of uniformly continuous completely positive semigroups
• Quantum Ito's formula and stochastic evolutions
• Fermion Ito's formula and stochastic evolutions
• The strong Markov property for fermion Brownian motion
• Covariant Markov dilations of quantum dynamical semigroups
• Stochastic integral representation of bounded quantum martingales in Fock space
• Unification of Fermion and Boson stochastic calculus
• Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae
• Quantum mechanical Wiener processes