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

Szymon Peszat

Studia Mathematica (1992)

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

Abstract

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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.

How to cite

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Peszat, 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

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  1. [1] S. Agmon, Lectures on Elliptic Boundary Value Problems, Van Nostrand, Princeton 1965. Zbl0142.37401
  2. [2] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, forthcoming book. Zbl0761.60052
  3. [3] E. B. Davies, One-Parameter Semigroups, London Math. Soc. Monographs 15, Academic Press, London 1980. Zbl0457.47030
  4. [4] E. Hille and R. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Colloq. Publ. 31, Providence, R.I., 1957. Zbl0078.10004
  5. [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. [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. [7] S. M. Kozlov, Some questions of stochastic partial differential equations, Trudy Sem. Petrovsk. 4 (1978), 147-172 (in Russian). 
  8. [8] H. H. Kuo, Gaussian Measures in Banach Spaces, Lecture Notes in Math. 463, Springer, Berlin 1975. Zbl0306.28010
  9. [9] S. Peszat, Equivalence of distribution of some Ornstein-Uhlenbeck processes taking values in Hilbert space, Probab. Math. Statist., to appear. Zbl0772.60029
  10. [10] J. Zabczyk, Law equivalence of Ornstein-Uhlenbeck processes, preprint 476, Inst. of Math., Polish Acad. of Sci., September 1990. 

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