# Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces

Studia Mathematica (1995)

- Volume: 115, Issue: 1, page 53-71
- ISSN: 0039-3223

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topFuhrman, Marco. "Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces." Studia Mathematica 115.1 (1995): 53-71. <http://eudml.org/doc/216198>.

@article{Fuhrman1995,

abstract = {We consider a semigroup acting on real-valued functions defined in a Hilbert space H, arising as a transition semigroup of a given stochastic process in H. We find sufficient conditions for analyticity of the semigroup in the $L^2(μ)$ space, where μ is a gaussian measure in H, intrinsically related to the process. We show that the infinitesimal generator of the semigroup is associated with a bilinear closed coercive form in $L^2(μ)$. A closability criterion for such forms is presented. Examples are also given.},

author = {Fuhrman, Marco},

journal = {Studia Mathematica},

keywords = {semigroup acting on real-valued functions defined in a Hilbert space; transition semigroup; stochastic process; Gaussian measure; bilinear closed coercive form; closability criterion},

language = {eng},

number = {1},

pages = {53-71},

title = {Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces},

url = {http://eudml.org/doc/216198},

volume = {115},

year = {1995},

}

TY - JOUR

AU - Fuhrman, Marco

TI - Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces

JO - Studia Mathematica

PY - 1995

VL - 115

IS - 1

SP - 53

EP - 71

AB - We consider a semigroup acting on real-valued functions defined in a Hilbert space H, arising as a transition semigroup of a given stochastic process in H. We find sufficient conditions for analyticity of the semigroup in the $L^2(μ)$ space, where μ is a gaussian measure in H, intrinsically related to the process. We show that the infinitesimal generator of the semigroup is associated with a bilinear closed coercive form in $L^2(μ)$. A closability criterion for such forms is presented. Examples are also given.

LA - eng

KW - semigroup acting on real-valued functions defined in a Hilbert space; transition semigroup; stochastic process; Gaussian measure; bilinear closed coercive form; closability criterion

UR - http://eudml.org/doc/216198

ER -

## References

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- [6] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Encyclopedia Math. Appl. 44, Cambridge University Press, 1992. Zbl0761.60052
- [7] M. Fuhrman, Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces, preprint, Dipartimento di Matematica, Politecnico di Milano, n. 105/p, ottobre 1993.
- [8] Z. M. Ma and M. Röckner, Dirichlet Forms, Springer, 1992.
- [9] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.
- [10] B. Schmuland, Non-symmetric Ornstein-Uhlenbeck processes in Banach space via Dirichlet forms, Canad. J. Math. 45 (1993), 1324-1338. Zbl0801.31003
- [11] A. Yagi, Coïncidence entre des espaces d'interpolation et des domaines de puissances fractionnaires d'opérateurs, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), 173-176. Zbl0563.46042
- [12] J. Zabczyk, Symmetric solutions of semilinear stochastic equations, in: Stochastic Partial Differential Equations and Applications, G. Da Prato and L. Tubaro (eds.), Lecture Notes in Math. 1390, Springer, 1989, 237-256.

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