Sommario
Si dimostra la convergenza al moto browniano di un processo stocastico ottenuto da un sistema meccanico unidimensionale, soggetto a condizioni iniziali aleatorie.
Summary
The convergence to the brownian motion of a stochastic process obtained by a onedimensional mechanical system, subject to random initial conditions, is proven.
This is a preview of subscription content, log in via an institution to check access.
References
Holley R.,The motion of a large particle, T.A.M.S. 144 (1969), 523–534
McLeish D.L.,Dependent central limit theorems and invariance principles, Annals of Probab., (2) 4 (1974), 620–628.
Billingsley P.,Convergence of probability measures, Wiley, New York, 1968.
Toscani G.,Diffusion with collision of a perfectly inelastic particle, Bollettino U.M.I. (6) 4-B (1985).
Spitzer F.,Uniform motion with elastic collision of an infinite particle system, J. Math. Mech., 18 (1969), 973–989.
Dobrushin R.L.,On Poisson's law for distributions of particles in space. Ukrain Math. Z.; 8 (1956), 127–134.
Stone C.,On a theorem of Dobrushin, Am. Math. Stat., 39, 1391–1401, (1968).
Ash R.B., Gardner M.F.,Topics in stochastic processes, Academic Press, London 1976.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gabetta, E. An invariance principle for one large particle with collisions. Meccanica 20, 272–275 (1985). https://doi.org/10.1007/BF02352678
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02352678