Geodesic
Gaussian white noise with trajectories in the space~$\mathcal S'(H)$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 3-11

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In this paper we construct a Gaussian white noise with trajectories in the space of generalized functions over $\mathcal S$ with values in a separable Hilbert space $H$. We obtain a solution to the Cauchy problem for a linear operator-differential equation with the additive white noise as a generalized random process with trajectories in the space of exponential distributions. We prove existence of the solution in the case when the operator coefficient $A$ generates a $C_0$ semigroup and in the case when $A$ generates an integrated semigroup.
Keywords: Gaussian white noise, generalized random process, semigroups of bounded operators. 
@article{IVM_2011_5_a0,
     author = {M. A. Alshanskii},
     title = {Gaussian white noise with trajectories in the space~$\mathcal S'(H)$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--11},
     publisher = {mathdoc},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_5_a0/}
}
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M. A. Alshanskii. Gaussian white noise with trajectories in the space~$\mathcal S'(H)$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 3-11. http://geodesic.mathdoc.fr/item/IVM_2011_5_a0/