By Takeyuki Hida
ISBN-10: 9812565264
ISBN-13: 9789812565266
This quantity contains papers via best mathematicians within the fields of stochastic research, white noise thought and quantum details, including their functions. The papers chosen have been offered on the foreign convention on Stochastic research: Classical and Quantum held at Meijo college, Nagoya, Japan from 1 to five November 2004. the massive variety of topics covers the newest learn in chance idea.
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Math. Phys. 14 (2002), 241-272. [7] T. Hida: “Analysis of Brownian Functionals,” Carleton Math. Lect. Notes, no. 13, Carleton University, Ottawa, 1975. [8] T. Hida: “Brownian Motion,” Springer-Verlag, 1980. [9] R. L. Hudson and K. R. Parthasarathy: Quantum Ito’s formula and stochastic evolutions, Commun. Math. Phys. 93 (1984), 301-323. [lo] R. L. Hudson and J. M. Lindsay: A non-commutative martingale representation theorem for non-Fock quantum Brownian motion, J. Funct. Anal. 61 (1985), 202-221.
J . Math. , 36(5):2135-2169, 1994. [3] S. N. Sengupta. A Mathematical Construction of the Non-Abelian Chern-Simons F'unctional Integral. Commun. Math. , 186:563-579,1997. [4] D. Altschuler and L. Freidel. Vassiliev knot invariants and Chern-Simons perturbation theory to all orders. Comm. Math. , 187:261-287, 1997. [5] S. M. Singer. Chern-Simons perturbation theory. , editor, Differential geometric methods in theoretical physics. Proceedings of the 20th international conference, June 3-7, 1991, New York City, NY, USA, volume 1-2, pages 3-45.
This work was supported by grant (No. R05-2004-000-11346-0) from the Basic Research Program of the Korea Science & Engineering Foundation. 1 White Noise Triplet Let H = L2 ( R +, d t)be the (complex) Hilbert space of L2-functions on R, = [O,m) with respect t o the Lebesgue measure d t and the norm of H is denoted by 1 . lo. Let A be a selfadjoint operator (densely defined) in H satisfying that there exist a sequence m ~ < X O ~ X ~ < X Z < . ( ,A - ' I I ; , = C X y 2 < m , j=O and an orthonormal basis { e j } g o of H such that Aej = A j e j .
Stochastic Analysis: Classical and Quantum: Perspectives of White Noise Theory by Takeyuki Hida
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