Fourier Asymptotics of Statistically Self-Similar Measures.
Fourier multipliers for non-symmetric Lévy processes
We study Fourier multipliers resulting from martingale transforms of general Lévy processes.
Fractional Brownian motion and the Markov property.
Fractional brownian sheet.
Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series
We introduce a fractional Langevin equation with α-stable noise and show that its solution is the stationary α-stable Ornstein-Uhlenbeck-type process recently studied by Taqqu and Wolpert. We examine the asymptotic dependence structure of via the measure of its codependence r(θ₁,θ₂,t). We prove that is not a long-memory process in the sense of r(θ₁,θ₂,t). However, we find two natural continuous-time analogues of fractional ARIMA time series with long memory in the framework of the Langevin...
Fractional multiplicative processes
Statistically self-similar measures on [0, 1] are limit of multiplicative cascades of random weights distributed on the b-adic subintervals of [0, 1]. These weights are i.i.d., positive, and of expectation 1/b. We extend these cascades naturally by allowing the random weights to take negative values. This yields martingales taking values in the space of continuous functions on [0, 1]. Specifically, we consider for each H∈(0, 1) the martingale (Bn)n≥1 obtained when the weights take the values −b−H...
Fractional Ornstein-Uhlenbeck processes.
Fractional Poisson processes and related planar random motions.
Fragmentation of ordered partitions and intervals.
Frequent points for random walks in two dimensions.
From a kinetic equation to a diffusion under an anomalous scaling
A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process on , where is the two-dimensional torus. Here is an autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance. is an additive functional of , defined as , where for small . We prove that the rescaled process converges in distribution to a two-dimensional Brownian motion. As a consequence, the appropriately...
From almost sure local regularity to almost sure Hausdorff dimension for gaussian fields
Fine regularity of stochastic processes is usually measured in a local way by local Hölder exponents and in a global way by fractal dimensions. In the case of multiparameter Gaussian random fields, Adler proved that these two concepts are connected under the assumption of increment stationarity property. The aim of this paper is to consider the case of Gaussian fields without any stationarity condition. More precisely, we prove that almost surely the Hausdorff dimensions of the range and the graph...
From shuffling cards to walking around the building: An introduction to modern Markov chain theory.
From Tanaka's formula to Ito's formula : distributions, tensor products and local times
Fubini's theorem for double Wiener integrals and the variance of the brownian path
Full-information best choice problems with imperfect observation and a random number of observations
Functional central limit theorems for seeds in a linear birth and growth model
A problem of heredity of mixing properties (α-mixing, β-mixing and ρ-mixing) from a stationary point process on ℝ × ℝ₊ to a sequence of some of its points called 'seeds' is considered. Next, using the mixing properties, several versions of functional central limit theorems for the distances between seeds and the process of the number of seeds are obtained.
Functional laws of the iterated logarithm for local times of recurrent random walks on
Functionals associated with self-intersections of the planar brownian motion
Functionals of spatial point processes having a density with respect to the Poisson process
-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Itô chaos expansion. In the second half we obtain more explicit results for a system of -statistics of some parametric models in stochastic geometry. In the logarithmic form functionals are connected to Gibbs models. There is an inequality between moments of Poisson...