Sample Size, Parameter Rates and Contiguity - The i.n.n.i.d. Case
Scaling limits of anisotropic Hastings–Levitov clusters
We consider a variation of the standard Hastings–Levitov model HL(0), in which growth is anisotropic. Two natural scaling limits are established and we give precise descriptions of the effects of the anisotropy. We show that the limit shapes can be realised as Loewner hulls and that the evolution of harmonic measure on the cluster boundary can be described by the solution to a deterministic ordinary differential equation related to the Loewner equation. We also characterise the stochastic fluctuations...
Second moment convergence rates for uniform empirical processes.
Semi-recorrido condicionado (expresión asintótica de la r-esperanza condicionada).
In a probability space (Ω,σ,P), for α ⊂ σ a sub-σ field, in general the best approximation in L∞ by elements of L∞(α) has not a unique solution. For the election between these, we prove the convergence P-almost surely of the conditional r-means, when r → ∞, to one solution, which we call conditional mid-range. This is characterized for each ω ∈ Ω by the mid-range, of one regular conditional distribution Q(ω, ·).
Slowdown estimates for ballistic random walk in random environment
We consider models of random walk in uniformly elliptic i.i.d. random environment in dimension greater than or equal to 4, satisfying a condition slightly weaker than the ballisticity condition . We show that for every and large enough, the annealed probability of linear slowdown is bounded from above by . This bound almost matches the known lower bound of , and significantly improves previously known upper bounds. As a corollary we provide almost sharp estimates for the quenched probability...
Small ball probabilities for stable convolutions
We investigate the small deviations under various norms for stable processes defined by the convolution of a smooth function with a real SαS Lévy process. We show that the small ball exponent is uniquely determined by the norm and by the behaviour of f at zero, which extends the results of Lifshits and Simon, Ann. Inst. H. Poincaré Probab. Statist.41 (2005) 725–752 where this was proved for f being a power function (Riemann-Liouville processes). In the Gaussian case, the same generality as...
Small deviations of iterated processes in the space of trajectories
We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes. When these conditions fail the asymptotics are quite different.
Small time asymptotics of Ornstein-Uhlenbeck densities in Hilbert spaces.
Some limit theorems of intermediate term of a random number of independent random variables
Some new Chacon-Edgar-type inequalities for stochastic processes, and characterizations of Vitali-conditions
Some remarks on Fourier seminorms
Some results on convergence rates for probabilities of moderate deviations for sums of random variables.
Sous-espaces symétriques des espaces d'Orlicz
Spectral norm of random large dimensional noncentral Toeplitz and Hankel matrices.
Spontaneous clustering in theoretical and some empirical stationary processes*
In a stationary ergodic process, clustering is defined as the tendency of events to appear in series of increased frequency separated by longer breaks. Such behavior, contradicting the theoretical “unbiased behavior” with exponential distribution of the gaps between appearances, is commonly observed in experimental processes and often difficult to explain. In the last section we relate one such empirical example of clustering, in the area of marine technology. In the theoretical part of the paper...
Statistical convergence of a sequence of random variables and limit theorems
In this paper the ideas of three types of statistical convergence of a sequence of random variables, namely, statistical convergence in probability, statistical convergence in mean of order and statistical convergence in distribution are introduced and the interrelation among them is investigated. Also their certain basic properties are studied.
Stochastic homogenization of nonconvex integral functionals
Suites de bi-probabilités stables
Sulla assoluta continuità di una variabile aleatoria la cui densità è limite di una successione di densità costanti a tratti
Sur la répartition des suites de Kakutani (I)