Asymptotic singular windings of ergodic diffusions
Let M be a complete connected oriented Riemannian manifold of dimension n [greater-or-equal, slanted] 3; let X be a symmetrizable ergodic diffusion on M; let y be an oriented compact submanifold of M, of codimension 2; let Nt be the linking number between y and X [0, t]; then t-1 Nt converges in law towards a Cauchy variable, whose parameter is calculated; this result is extended mainly to the stochastic bridge, to the finite marginals of the processes (Xrt, t-1 Nrt), and to the integral along X[0, t] of [omega] [epsilon] H1 (M/y)/H1 (M).
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Volume (Year): 62 (1996)
Issue (Month): 2 (July)
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- Franchi, J., 1994. "Enroulements asymptotiques du mouvement brownien autour de lacets dans une variété riemannienne compacte de dimension 3," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 251-272, August.
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