Non-commutative Burgers equation

Hokkaido Mathematical Journal

Volumn 25, Issue 2, 1996, Pages 315-332

  Dermoune, Azzouz ^a  

^a UNIVERSITÉ DU MAINE   (France)

Author keywords

Burgers equation; Fock space; Gaussian white noise; Poissonian white noise

Indexed keywords

EID: 0038974453     PISSN: 03854035     EISSN: None     Source Type: Journal    
DOI: 10.14492/hokmj/1351516727     Document Type: Article

References (17)

1. Albeverio S., Molchanov S.A. and Surgailis D., Stratified structure of the Universe and Burgers equation-a probabilistic approach. Probab. Theory Relat. Fields 100 (1994), 457-484.
2. Berezin F.A., The method of second quantization. Academic Press (1966).
3. Cole, J.D., On a quasi-linear parabolic equation occuring in aerodynamics. Quart. Appl Math. 9 (1951), 225-236.
4. Do Prato G., Debussche A. and Temam R., Stochastic Burger expiation. NoDEA 1 (1994), 389-402.
5. Deimoune A., Stochastic heat equation with Gaussian or Poissonian white noise. Preprint (1994).
6. Gärtner J. and Molchanov S.A., Parabolic problem for Anderson model. Commun. Math. Phys. 132 (1992), 613-655.
7. Hida T. and Ikeda N., Analysis on Hilbert space with reproducing kernel arising from multiple Wiener integral. Proc. Ffth Berkeley Symp. Math. Stat. Probab. II, Part 1 (1965), 117-143.
8. Hida T., Kuo H.H., Potthof J. and Streit L., White Noise Analysis. Kluwer (1993).
9. Holden H., Lindstrom T., Oksendal B., Uboe J. and Zhang T.S., The Burgers equation with a noisy force and the stochastic heat equation. Comm. PDE. 19 (1994), 119-141.
10. xx., Commun. Pure Appl. Math. 3 (1950), 201-230.
11. Ito K., Multiple Wiener integral. J. Math. Soc. Japan. 3 (1951), 157-169.
12. Krée P. and Raczka R., Kernel and symbol in quantum field theory. Ann. Inst. H. Poincaré. Section A, Vol. 28, Numéro 1, (1978). 41-73.
13. Meyer P.A. Élements de probabilités quantiques. Sém. Prob. XX, Springer LN, Vol. 1204.
14. Neveu J., Processus aléatoires Gaussiens. Les Presses de l’Univ. de Montréal (1968).
15. Nualart D. and Zakai M., Generalized Brownian functionals and the solution to a stochastic partial differential equation. J. Functional Analysis 84 (1989), 279-296.
16. Surgailis D., On multiple Poisson stochastic integrals and associated Markov Semigroups. Probability and Math. Stat. 3, Fasc. 2, (1984) 217-239.
17. Wick G.C, The evaluation of the collision matrix. Phys. Rev. 80 (1950), 268-272.