Calcul stochastique non-commutatif

[1]  N. Wiener.  The Homogeneous Chaos , 1938 .

[2]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[3]  Kiyosi Itô.  Multiple Wiener Integral , 1951 .

[4]  J. Neumann.  Mathematical Foundations of Quantum Mechanics , 1955 .

[5]  J. Cooper,et al.  Les Algebres d'Operateurs dans l'Espace Hilbertien , 1958 .

[6]  Sterling K. Berberian,et al.  Introduction to Hilbert Space , 1977 .

[7]  David Shale,et al.  LINEAR SYMMETRIES OF FREE BOSON FIELDS( , 1962 .

[8]  Jean-Pierre Serre.  Algèbres de Lie semi-simples complexes , 1966 .

[9]  N. Vilenkin.  Special Functions and the Theory of Group Representations , 1968 .

[10]  P. Meyer,et al.  Méthodes de martingales et théorie des flots , 1971 .

[11]  R. Leighton,et al.  Feynman Lectures on Physics , 1971 .

[12]  Jim Pitman.  ONE-DIMENSIONAL BROWNIAN MOTION AND THE THREE-DIMENSIONAL BESSEL PROCESS , 1974 .

[13]  A. Skorokhod.  On a generalization of the stochastic integral , 1976 .

[14]  E. B. Davies.  Quantum theory of open systems , 1976 .

[15]  John T. Lewis,et al.  Dilations of dynamical semi-groups , 1976 .

[16]  M. Vergne,et al.  The Weil representation, Maslov index, and theta series , 1980 .

[17]  B. Gaveau,et al.  L'intégrale stochastique comme opérateur de divergence dans l'espace fonctionnel , 1982 .

[18]  L. Rogers.  Stochastic differential equations and diffusion processes: Nobuyuki Ikeda and Shinzo Watanabe North-Holland, Amsterdam, 1981, xiv + 464 pages, Dfl.175.00 , 1982 .

[19]  R. Streater,et al.  The Itô-Clifford integral , 1982 .

[20]  Luigi Accardi,et al.  Quantum Stochastic Processes , 1982 .

[21]  Ruth J. Williams,et al.  Introduction to Stochastic Integration , 1994 .

[22]  Robin L. Hudson,et al.  Quantum Ito's formula and stochastic evolutions , 1984 .

[23]  渡辺 信三.  Lectures on stochastic differential equations and Malliavin calculus , 1984 .

[24]  G. Vincent-smith.  Dilation of a Dissipative Quantum Dynamical System to a Quantum Markov Process , 1984 .

[25]  S. Sternberg,et al.  Symplectic Techniques in Physics , 1984 .

[26]  H. Maassen.  Quantum Markov processes on Fock space described by integral kernels , 1985 .

[27]  Robin L. Hudson,et al.  Unification of fermion and Boson stochastic calculus , 1986 .

[28]  P. Meyer,et al.  Une martingale d'operateurs bornés, non representable en integrale stochastique , 1986 .

[29]  J. Sauvageot.  Markov quantum semigroups admit covariant MarkovC*-dilations , 1986 .

[30]  K.R Parthasarathy,et al.  Stochastic Integral Representation of Bounded Quantum Martingales in Fock Space , 1986 .

[31]  K. Parthasarathy,et al.  Representation of a class of quantum martingales II , 1988 .

[32]  Dénes Petz,et al.  Conditional expectation in quantum probability , 1988 .

[33]  D. Nualart.  Nonclausal stochastic integrals and calculus , 1988 .

[34]  Multidimensional quantum diffusions , 1988 .

[35]  P. Meyer.  Elements de probabilites quantiques , 1989 .

[36]  M. Émery,et al.  On the Azéma martingales , 1989 .

[37]  M. Evans.  Existence of quantum diffusions , 1989 .

[38]  P. Protter.  Stochastic integration and differential equations : a new approach , 1990 .

[39]  W. V. Waldenfels.  The Markov process of total spins , 1990 .

[40]  Serge Reynaud.  Introduction à la réduction du bruit quantique , 1990 .

[41]  P. Biane.  Chaotic representation for finite Markov chains , 1990 .

[42]  K. Parthasarathy.  A generalised biane process , 1990 .

[43]  R. Speicher.  A new example of ‘independence’ and ‘white noise’ , 1990 .

[44]  K. Parthasarathy,et al.  Markov chains as evans-hudson diffusions in fock space , 1990 .

[45]  J. Sauvageot.  Quantum dirichlet forms, differential calculus and semigroups , 1990 .

[46]  Philippe Biane.  Marches de Bernoulli quantiques , 1990 .

[47]  K. Parthasarathy,et al.  UNIFICATION OF QUANTUM NOISE PROCESSES IN FOCK SPACES , 1991 .

[48]  V. Belavkin.  A quantum nonadapted Ito formula and stochastic analysis in Fock scale , 1991, math-ph/0512076.

[49]  The Azéma martingales as components of quantum independent increment processes , 1991 .

[50]  Quantum random walk on the dual of SU (n) , 1991 .

[51]  D. Applebaum.  Unitary evolutions and horizontal lifts in quantum stochastic calculus , 1991 .

[52]  Roland Speicher,et al.  An example of a generalized Brownian motion , 1991 .

[53]  M. Émery.  Quelques cas de représentation chaotique , 1991 .

[54]  Stochastic integration on the full Fock space with the help of a kernel calculus , 1991 .

[55]  D. Applebaum.  An operator theoretic approach to stochastic flows on manifolds , 1992 .

[56]  J. Maria,et al.  Integrator properties of the skorohod integral , 1992 .

[57]  V. Belavkin.  Chaotic states and stochastic integration in quantum systems , 1992, math/0512265.

[58]  K. Parthasarathy.  An Introduction to Quantum Stochastic Calculus , 1992 .

[59]  F. Fagnola,et al.  Quantum Flows with Unbounded Structure Maps and Finite Degrees of Freedom , 1993 .

[60]  R. Hudson,et al.  Casimir chaos in a boson Fock space , 1994 .

[61]  B. V. Rajarama Bhat,et al.  Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory , 1995 .

[62]  J. Sauvageot.  Semi-groupe de la chaleur transverse sur laC*-algèbre d'un feuilletage riemannien , 1996 .