Results 11 to 20 of about 182 (33)
Stationary Quantum Markov processes as solutions of stochastic differential equations
, 1998 From the operator algebraic approach to stationary (quantum) Markov processes there has emerged an axiomatic definition of quantum white noise. The role of Brownian motion is played by an additive cocycle with respect to its time evolution.
Jürgen Hellmich +2 more
semanticscholar +1 more source
Quantum stochastic convolution cocycles III [PDF]
, 2011 Every Markov-regular quantum Levy process on a multiplier C*-bialgebra is shown to be equivalent to one governed by a quantum stochastic differential equation, and the generating functionals of norm-continuous convolution semigroups on a multiplier C ...
Lindsay, J. Martin, Skalski, Adam G.
core +2 more sources
Monotone independence, comb graphs and Bose-Einstein condensation [PDF]
, 2004 The adjacency matrix of a comb graph is decomposed into a sum of monotone independent random variables with respect to the vacuum state. The vacuum spectral distribution is shown to be asymptotically the arcsine law as a consequence of the monotone ...
Accardi, L., Ben Ghorbal, A., Obata, N.
core +1 more source
The Quantum Black-Scholes Equation [PDF]
, 2006 Motivated by the work of Segal and Segal on the Black-Scholes pricing formula in the quantum context, we study a quantum extension of the Black-Scholes equation within the context of Hudson-Parthasarathy quantum stochastic calculus.
Accardi, Luigi, Boukas, Andreas
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Approximation of quantum Levy processes by quantum random walks [PDF]
, 2007 Every quantum Levy process with a bounded stochastic generator is shown to arise as a strong limit of a family of suitably scaled quantum random walks.Comment: 7 ...
Franz, Uwe, Skalski, Adam
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Classical dilations \`a la Hudson-Parthasarathy of Markov semigroups
, 2007 We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup defined in Quantum Probability via quantum stochastic differential equations.
Gregoratti, M.
core +2 more sources
Analysis of unbounded operators and random motion
, 2009 We study infinite weighted graphs with view to \textquotedblleft limits at infinity,\textquotedblright or boundaries at infinity. Examples of such weighted graphs arise in infinite (in practice, that means \textquotedblleft very\textquotedblright large ...
Dunford N. +6 more
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Unbounded operators, Lie algebras, and local representations
, 2014 We prove a number of results on integrability and extendability of Lie algebras of unbounded skew-symmetric operators with common dense domain in Hilbert space.
Jorgensen, Palle, Tian, Feng
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Quantum Feynman-Kac perturbations
, 2013 We develop fully noncommutative Feynman-Kac formulae by employing quantum stochastic processes. To this end we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles.
Belton, Alexander C. R. +2 more
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Universal Malliavin calculus in Fock and Levy-Ito spaces [PDF]
, 2008 We review and extend Lindsay's work on abstract gradient and divergence operators in Fock space over a general complex Hilbert space. Precise expressions for the domains are given, the L2-equivalence of norms is proved and an abstract version of the It^o-
Applebaum, D.
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