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In the present paper, we consider the Langevin equation driven by a linear fractional stable motion noise, which is a selfsimilar process with long-range dependence but does not
Key words: random fields, Gaussian processes, fractional Brownian motion, fractal mea- sures, self–similar measures, small deviations, Kolmogorov numbers, metric entropy,
The expression just obtained for the distribution of coalescing Brownian motions is closely related to the formula for the transition density of the interlaced Brownian motions given
Nualart: Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H in (0,1/2), preprint.. Victoir, Good Rough Path Sequences
Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process.. (2)
(We remind the reader that a set is called totally disconnected if it contains no connected component larger than one point.) The fractals we study are defined as the complement of
We present a tail inequality for suprema of empirical processes generated by vari- ables with finite ψ α norms and apply it to some geometrically ergodic Markov chains to derive
When X and Y are Brownian motions on a Riemannian manifold, Kendall [3] and Cranston [1] constructed a coupling by using the Riemannian geometry of the underlying space.. Their
