By Takeyuki Hida

This quantity comprises papers via prime mathematicians within the fields of stochastic research, white noise thought and quantum details, including their functions. The papers chosen have been awarded on the overseas convention on Stochastic research: Classical and Quantum held at Meijo collage, Nagoya, Japan from 1 to five November 2004. the big variety of matters covers the newest study in chance idea.

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Sci. (Paris) 146 (1908), 530-533 [7] Jean Perrin; Movement Brownien et Rkartik Molkculaire, Annales de Chimie et Pyisique, 8"" sBries, Septembre (1909) [8]Jean Perrin; Les Atomes. Felix Alcan, Paris, Nouvelle collection scientifique, directeur Emile Bore1 (1912) [9] Norbert Wiener; Differential-Space, J. Math. , 2 (1923), 131-174 [lo] Gorge Eugene Uhlenbeck and Leonard Salomon Ornstein; On the theory of Brownian motion, Physical Review 36 (1930), 823-841. 1111 Norbert Wiener; The homogeneous chaos, Amer.

M. R. Parthasarathy: Stochastic integral representation of some quantum martingales in Fock space, in “From Local Times to Global Geometry, Control and Physics,” Proc. Warwick Symposium 1984/1985, pp. 121-131, Pitman RNM, 1986. [12] U. C. Ji: Stochastic integral representation theorem for quantum semimartingales, J. Func. Anal. 201 (2003), 1-29. [13] U. C. Ji and N. Obata: Quantum white noise calculus, in “Non-Commutativity, InfiniteDimensionality and Probability at the Crossroads (N. Obata, T.

Hudson, J. M. R. Parthasarathy: Stochastic integral representation of some quantum martingales in Fock space, in “From Local Times to Global Geometry, Control and Physics,” Proc. Warwick Symposium 1984/1985, pp. 121-131, Pitman RNM, 1986. [12] U. C. Ji: Stochastic integral representation theorem for quantum semimartingales, J. Func. Anal. 201 (2003), 1-29. [13] U. C. Ji and N. Obata: Quantum white noise calculus, in “Non-Commutativity, InfiniteDimensionality and Probability at the Crossroads (N.