Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 9 (2004) > Paper 4 open journal systems 


Finite dimensional determinants as characteristic functions of quadratic Wiener functionals

Keisuke Hara,


Abstract
We show a method and the structure to calculate the characteristic functions of quadratic Wiener functionals by using classical Weierstrass-Hadamard's theory on entire functions. We also examine the idea by an example for Gaussian processes with multiple Markovian property.


Full text: PDF

Pages: 26--35

Published on: March 22, 2004


Bibliography
  1. T. Chan. Indefinite quadratic functions of Gaussian processes as least action paths. Ann. Inst. H. Poincaré Probab. Statist. 27 No.2, (1991), 239--271. Math. Review 1118937 (93d:60063)
  2. S. Coleman. The Uses of Instantons. in The Whys of Subnuclear Physics" (Erice, 1977, Ed. A.~Zichichi), Plenum, New York, (1979), 805--941.
  3. K. Hara and N. Ikeda. Quadratic Wiener functionals and dynamics on Grassmannians. Bull. Sci. math. 125, No.6-7, (2001), 481--528. Math. Review 1869989 (2002j:60151)
  4. N. Ikeda, S. Kusuoka, and S. Manabe. Lévy's stochastic area formula for Gaussian processes. Comm. Pure and Applied Math., XLVII, (1994), 329--360. Math. Review 1266245 (95h:60086)
  5. N. Ikeda, S. Kusuoka, and S. Manabe. Lévy's stochastic area formula and Related Problems. Proc. Pure. Math. AMS 57, (1995), 281--305. Math. Review 1335477 (96f:60092)
  6. N. Ikeda and S. Manabe. Asymptotic formulae for stochastic oscillatory integrals. in Proceeding of the Taniguchi International Symposium on Asymptotic Problems in Probability Theory (Sanda and Kyoto, Ed., K.~D.~Elworthy and N.~Ikeda), Pitman Research Note in Math., 284, Logman, Essex, (1993). Math. Review 1354166 (97j:60098)
  7. N. Ikeda and S. Manabe. Van Vleck-Pauli formula for Wiener integrals and Jacobi fields, in Itô's Stochastic calculus and Probability theory", Springer, (1996), 141--156. Math. Review 1439522 (98g:81110)
  8. N. Ikeda and S. Taniguchi. Quadratic Wiener functionals, Kalman-Bucy filters, and the KdV equation, in Stochastic Analysis and Related Topics in Kyoto (Kyoto, 2002), Advanced Studies in Pure Mathematics, to appear.
  9. H. Matsumoto and S. Taniguchi. Wiener functionals of second order and their Lévy measures. Electronic Journal of Probability 7, No.14, (2002), 1--30. Math. Review 1921743 (2003f:60145)















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X