Asymptotic singular windings of ergodic diffusions. (English) Zbl 0863.58072
Summary: Let \(M\) be a complete connected oriented Riemannian manifold of dimension \(n\geq 3;\) let \(X\) be a symmetrizable ergodic diffusion of \(M\); let \(\mathcal L\) be an oriented compact submanifold of \(M,\) of codimension 2; let \(\mathcal N_t\) be the linking number between \(\mathcal L\) and \(X[0,t]\); then \(t^{-1} \mathcal N_t\) 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 \((X_{rt},t^{-1}\mathcal N_{rt}),\) and to the integral along \(X[0,t]\) of \(\omega \in H^1(M\backslash \mathcal L)/H^1(M).\)
Keywords:
ergodic diffusion; Riemannian manifold; winding numbers; stochastic line integrals; asymptotic lawReferences:
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