Standard

Gaussian white noise with trajectories in the space S′(H). / Al’shanskii, M. A.
In: Russian Mathematics, Vol. 55, No. 5, 01.05.2011, p. 1-7.

Research output: Contribution to journal › Article › peer-review

Harvard

Al’shanskii, MA 2011, 'Gaussian white noise with trajectories in the space S′(H)', Russian Mathematics, vol. 55, no. 5, pp. 1-7. https://doi.org/10.3103/S1066369X1105001X

APA

Al’shanskii, M. A. (2011). Gaussian white noise with trajectories in the space S′(H). Russian Mathematics, 55(5), 1-7. https://doi.org/10.3103/S1066369X1105001X

Vancouver

Al’shanskii MA. Gaussian white noise with trajectories in the space S′(H). Russian Mathematics. 2011 May 1;55(5):1-7. doi: 10.3103/S1066369X1105001X

Author

Al’shanskii, M. A. / Gaussian white noise with trajectories in the space S′(H). In: Russian Mathematics. 2011 ; Vol. 55, No. 5. pp. 1-7.

BibTeX

@article{c531e7f235884763b4334cd09ad6f806,
title = "Gaussian white noise with trajectories in the space S′(H)",
abstract = "In this paper we construct a Gaussian white noise with trajectories in the space of generalized functions over S with values in a separable Hilbert space H. We obtain a solution to the Cauchy problem for a linear differential-operator equation with additive white noise as a generalized random process with trajectories in the space of exponential distributions. We prove the existence of a solution in the case when the operator coefficient A generates a C 0-semigroup and in the case when A generates an integrated semigroup.",
author = "Al{\textquoteright}shanskii, {M. A.}",
note = "This work was supported by the Russian Foundation for Basic Research, grant No. 06-03-00148, and the Ministry of Education and Science of the Russian Federation, grant No. 2.1.1/2000.",
year = "2011",
month = may,
day = "1",
doi = "10.3103/S1066369X1105001X",
language = "English",
volume = "55",
pages = "1--7",
journal = "Russian Mathematics",
issn = "1066-369X",
publisher = "Pleiades Publishing",
number = "5",

}

RIS

TY - JOUR

T1 - Gaussian white noise with trajectories in the space S′(H)

AU - Al’shanskii, M. A.

N1 - This work was supported by the Russian Foundation for Basic Research, grant No. 06-03-00148, and the Ministry of Education and Science of the Russian Federation, grant No. 2.1.1/2000.

PY - 2011/5/1

Y1 - 2011/5/1

N2 - In this paper we construct a Gaussian white noise with trajectories in the space of generalized functions over S with values in a separable Hilbert space H. We obtain a solution to the Cauchy problem for a linear differential-operator equation with additive white noise as a generalized random process with trajectories in the space of exponential distributions. We prove the existence of a solution in the case when the operator coefficient A generates a C 0-semigroup and in the case when A generates an integrated semigroup.

AB - In this paper we construct a Gaussian white noise with trajectories in the space of generalized functions over S with values in a separable Hilbert space H. We obtain a solution to the Cauchy problem for a linear differential-operator equation with additive white noise as a generalized random process with trajectories in the space of exponential distributions. We prove the existence of a solution in the case when the operator coefficient A generates a C 0-semigroup and in the case when A generates an integrated semigroup.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=80051619328

U2 - 10.3103/S1066369X1105001X

DO - 10.3103/S1066369X1105001X

M3 - Article

VL - 55

SP - 1

EP - 7

JO - Russian Mathematics

JF - Russian Mathematics

SN - 1066-369X

IS - 5

ER -

ID: 38004499