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Normes hölderiennes et support des diffusions. (Hölder norms and the support theorem for diffusions). (French) Zbl 0768.60067
Summary: We show that the Stroock-Varadhan support theorem [D. W. Stroock and S. R. S. Varadhan, Proc. 6th Berkeley Sympos. Math. Statist. Probab., Univ. Calif. 1970, 3, 333-359 (1972; Zbl 0255.60056)], is valid in \(\alpha\)-Hölder norm, \(\alpha<1/4\) (Theorem 2). The central tool is an estimate (stated in Theorem 1 and in Corollary 1) of the probability that the Brownian motion has a large Hölder norm but a small uniform norm. This estimate is obtained by using Ciesielski’s theorem [see P. Baldi and B. Roynette, Probab. Theory Relat. Fields 93, No. 4, 457-484 (1992; Zbl 0767.60078), for other applications of this theorem].

60J60 Diffusion processes