Quantum stochastic dynamics. I.
Majewski, Adam W., Zegarlinski, Boguslaw (1995)
Mathematical Physics Electronic Journal [electronic only]
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Displaying similar documents to “Continuous interpolation of solution sets of Lipschitzian quantum stochastic differential inclusions.”
Quantum stochastic dynamics. I.
Quantum stochastic differential equations driven by free noises and dilations of markovian semigroups
Maria Elvira Mancino (1994)
Rendiconti del Seminario Matematico della Università di Padova
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Quantum stochastic convolution cocycles I
J. Martin Lindsay, Adam G. Skalski (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Q-adapted quantum stochastic integrals and differentials in Fock scale
Viacheslav Belavkin, Matthew Brown (2011)
Banach Center Publications
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In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic (QS) integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures, on a space-time σ-field , of the QS integration. Then rigorous analysis of the QS integrals is carried out, and continuity of the QS derivative D is proved. Finally, Q-adapted dynamics is discussed, including Bosonic (Q = I), Fermionic (Q = -I), and monotone...
Backward stochastic differential equations with oblique reflection and local Lipschitz drift.
Aman, Auguste, N'Zi, Modeste (2003)
Journal of Applied Mathematics and Stochastic Analysis
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Introduction to the Theory of the It-type Stochastic Integrals and Stochastic Differential Equations
Svetlana Janković (1998)
Zbornik Radova
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Approximation by time discretization of special stochastic evolution equations.
Lisei, Hannelore (2001)
Mathematica Pannonica
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Quantum stochastic convolution cocycles -algebraic and C*-algebraic
J. Martin Lindsay, Adam G. Skalski (2006)
Banach Center Publications
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We summarise recent results concerning quantum stochastic convolution cocycles in two contexts-purely algebraic and C*-algebraic. In each case the class of cocycles arising as the solution of a quantum stochastic differential equation is characterised and the form taken by the stochastic generator of a *-homomorphic cocycle is described. Throughout the paper a common viewpoint on the algebraic and C*-algebraic situations is emphasised; the final section treats the unifying example of...
Mild solutions of quantum stochastic differential equations.
Fagnola, Franco, Wills, Stephen J. (2000)
Electronic Communications in Probability [electronic only]
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Feynman diagrams and the quantum stochastic calculus
John Gough (2006)
Banach Center Publications
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We present quantum stochastic calculus in terms of diagrams taking weights in the algebra of observables of some quantum system. In particular, we note the absence of non-time-consecutive Goldstone diagrams. We review recent results in Markovian limits in these terms.
Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients
Dorel Barbu, Gheorghe Bocşan (2002)
Czechoslovak Mathematical Journal
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In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.
Existence of viable solutions for a nonconvex stochastic differential inclusion
Benoit Truong-Van, Truong Xuan Duc Ha (1997)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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For the stochastic viability problem of the form dx(t) ∈ F(t,x(t))dt+g(t,x(t))dW(t), x(t) ∈ K(t), where K, F are set-valued maps which may have nonconvex values, g is a single-valued function, we establish the existence of solutions under the assumption that F and g possess Lipschitz property and satisfy some tangential conditions.