Law equivalence of solutions of some linear stochastic equations in Hilbert spaces

• Autorzy: Szymon Peszat
• Języki publikacji: EN

Abstrakty

EN

Sufficient and necessary conditions for equivalence of the distributions of the solutions of some linear stochastic equations in Hilbert spaces are given. Some facts in the theory of perturbations of semigroup generators and Zabczyk's results on law equivalence are used.

Kategorie tematyczne

• 60G15: Gaussian processes
• 60H15: Stochastic partial differential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1991-1992
• Tom: 101
• Numer: 3
• Strony: 269-284

Daty

wydano

1992

otrzymano

1991-01-14

poprawiono

1991-09-17

poprawiono

1991-11-18

Twórcy

autor

Szymon Peszat

• Institute of Mathematics, University of Mining and Metallurgy, Al. Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

• [1] S. Agmon, Lectures on Elliptic Boundary Value Problems, Van Nostrand, Princeton 1965.
• [2] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, forthcoming book.
• [3] E. B. Davies, One-Parameter Semigroups, London Math. Soc. Monographs 15, Academic Press, London 1980.
• [4] E. Hille and R. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Colloq. Publ. 31, Providence, R.I., 1957.
• [5] T. Koski and W. Loges, Asymptotic statistical inference for a stochastic heat flow problem, Statist. Probab. Lett. 3 (1985), 185-189.
• [6] S. M. Kozlov, Equivalence of measures for Ito's partial differential equations, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1977 (4), 147-152 (in Russian).
• [7] S. M. Kozlov, Some questions of stochastic partial differential equations, Trudy Sem. Petrovsk. 4 (1978), 147-172 (in Russian).
• [8] H. H. Kuo, Gaussian Measures in Banach Spaces, Lecture Notes in Math. 463, Springer, Berlin 1975.
• [9] S. Peszat, Equivalence of distribution of some Ornstein-Uhlenbeck processes taking values in Hilbert space, Probab. Math. Statist., to appear.
• [10] J. Zabczyk, Law equivalence of Ornstein-Uhlenbeck processes, preprint 476, Inst. of Math., Polish Acad. of Sci., September 1990.