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

Studia Mathematica (1992)

- Volume: 101, Issue: 3, page 269-284
- ISSN: 0039-3223

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topPeszat, Szymon. "Law equivalence of solutions of some linear stochastic equations in Hilbert spaces." Studia Mathematica 101.3 (1992): 269-284. <http://eudml.org/doc/215905>.

@article{Peszat1992,

abstract = {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.},

author = {Peszat, Szymon},

journal = {Studia Mathematica},

keywords = {cylindrical Wiener process; stochastic equations in Hilbert spaces; perturbations of semigroup generators; law equivalence},

language = {eng},

number = {3},

pages = {269-284},

title = {Law equivalence of solutions of some linear stochastic equations in Hilbert spaces},

url = {http://eudml.org/doc/215905},

volume = {101},

year = {1992},

}

TY - JOUR

AU - Peszat, Szymon

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

JO - Studia Mathematica

PY - 1992

VL - 101

IS - 3

SP - 269

EP - 284

AB - 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.

LA - eng

KW - cylindrical Wiener process; stochastic equations in Hilbert spaces; perturbations of semigroup generators; law equivalence

UR - http://eudml.org/doc/215905

ER -

## References

top- [1] S. Agmon, Lectures on Elliptic Boundary Value Problems, Van Nostrand, Princeton 1965. Zbl0142.37401
- [2] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, forthcoming book. Zbl0761.60052
- [3] E. B. Davies, One-Parameter Semigroups, London Math. Soc. Monographs 15, Academic Press, London 1980. Zbl0457.47030
- [4] E. Hille and R. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Colloq. Publ. 31, Providence, R.I., 1957. Zbl0078.10004
- [5] T. Koski and W. Loges, Asymptotic statistical inference for a stochastic heat flow problem, Statist. Probab. Lett. 3 (1985), 185-189. Zbl0589.62075
- [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. Zbl0306.28010
- [9] S. Peszat, Equivalence of distribution of some Ornstein-Uhlenbeck processes taking values in Hilbert space, Probab. Math. Statist., to appear. Zbl0772.60029
- [10] J. Zabczyk, Law equivalence of Ornstein-Uhlenbeck processes, preprint 476, Inst. of Math., Polish Acad. of Sci., September 1990.

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