Geodesic
Poissonian subordinators, the Wiener–Ornstein–Uhlenbeck field, and a relation between the Ornstein–Uhlenbeck processes and the Brownian bridges
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 225-237 
O. V. Rusakov. Poissonian subordinators, the Wiener–Ornstein–Uhlenbeck field, and a relation between the Ornstein–Uhlenbeck processes and the Brownian bridges. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 225-237. http://geodesic.mathdoc.fr/item/ZNSL_2010_384_a11/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

To a sequence of i.i.d. random variables we apply the time change operator via the independent of this sequence Poisson process. We consider the sums of the independent copies of a such kind constructed processes having the continuous time. The finite dimensional distributions of the limits of these sums coincide with the finite dimensional distributions of the Wiener–Ornstein–Uhlenbeck field which is the tensor product of the Brownian motion and the Ornstein–Uhlenbeck process. The transition characteristics of the limiting process are described by the Brownian bridges which are built into the Wiener–Ornstein–Uhlenbeck field. Bibl. 4 titles.

[1] P. Billingsli, Skhodimost veroyatnostnykh mer, Nauka, M., 1977 | MR

[2] O. V. Rusakov, “Summy nezavisimykh puassonovskikh subordinatorov i ikh svyaz so strogo $\alpha$-ustoichivymi protsessami tipa Ornshteina–Ulenbeka”, Zap. nauchn. semin. POMI, 361, 2008, 123–137 | Zbl

[3] U. Feller, Vvedenie v teoriyu veroyatnostei i ee primeneniya, v. 2, Nauka, M., 1984

[4] O. Vasićek, “An equilibrium characterization of the term structure”, J. Financial Economics, 5 (1977), 177–188 | DOI