Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-25T00:13:18.804Z Has data issue: false hasContentIssue false
  • English
  • Français

Smoothness of solutions of stochastic evolution equations and the existence of a filtering transition density

Published online by Cambridge University Press:  22 January 2016

B. L. Rozovskii  and
A. Shimizu
B. L. Rozovskii
Affiliation:
A. Shimizu
Affiliation:
Nagoya Institute of Technology, Nagoya 466, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we shall discuss the smoothness of solutions of stochastic evolution equations, which has been investigated in N. V. Krylov and B. L. Rozovskii [2] [3], to establish the existence of a filtering transition density.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 84 , December 1981 , pp. 195 - 208
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

[ 1 ] Fujisaki, M. Kallianpur, G. and Kunita, H., Stochastic differential equations for the non-linear filtering problem, Osaka J. Math., 9 (1972), 19–42.Google Scholar
[ 2 ] Krylov, N.V. and Rozovskii, B.L., On Cauchy problem for linear stochastic partial differential equations, Izv. Akad. Nauk SSSR, Ser. Mat., 41 (1977), 1329–1347; English transl, in Math. USSR Izv., 11 (1977).Google Scholar
[ 3 ] Krylov, N.V. and Rozovskii, B.L., On conditional distributions of diffusion processes, Izv. Akad. Nauk SSSR, Ser. Mat., 42 (1978), 356–378; English transl, in Math. USSR Izv., 12 (1978).Google Scholar
[ 4 ] Krylov, N.V. and Rozovskii, B.L., Ito’s equations in Banach spaces and strongly parabolic stochastic partial differential equations, Doklady Akad. Nauk, 249 (1979), 285–289.Google Scholar
[ 5 ] Krylov, N.V. and Rozovskii, B.L., On stochastic evolution equations, Sovremennye problemy matematiki, 14, Itogi nauki i tekhniki (1979).Google Scholar
[ 6 ] Liptser, R.S. and Shiryayev, A.N., Statistics of random processes, Nauka, Moscow, 1974; English transi. Vols. I, II, Springer-Verlag, 1977.Google Scholar
[ 7 ] Mckean, H.P. Jr., Stochastic integrals, Academic press, 1969.Google Scholar
[ 8 ] Nirenberg, L., On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, 13 (1959), 115–162.Google Scholar
[ 9 ] Pardoux, E., Filtrage de diffusions avec conditions frontières, caractérisation de la densité conditionelle, Journées de Statistique des Processus Stochastiques, Lecture Notes in Mathematics, 636, Springer-Verlag (1977), 163–188.Google Scholar