Related papers: The strong renewal theorem with infinite mean via …
For real power series whose non-zero coefficients satisfy $|a_m|^{1/m}\to~1$ we prove a stronger version of Fabry theorem relating the frequency of sign changes in the coefficients and analytic continuation of the sum of the power series.
In this paper we prove that, under certain conditions, a strong law of large numbers holds for a class of super-diffusions $X$ corresponding to the evolution equation $\partial_t u_t=L u_t+\beta u_t-\psi(u_t)$ on a bounded domain $D$ in…
We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…
This paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near-epoch dependent sequences. Using these limiting theorems, we develop a general asymptotic theory on the Wald…
Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and,…
We show that for every "locally finite" unit-preserving completely positive map P acting on a C*-algebra, there is a corresponding *-automorphism \alpha of another unital C*-algebra such that the two sequences P, P^2,P^3,... and \alpha,…
We prove a conjecture by Vemuri by proving sharp bounds on $\ell^{\kappa}$ sums of Hermite functions multiplied by an exponentially decaying factor. More explicitly, we prove that, for each $y>0,$ we have \[ \sum_{n \ge 1} |h_n(x)|^{\kappa}…
Under certain general conditions, we prove that the stable central limit theorem holds in the total variation distance and get its optimal convergence rate for all $\alpha \in (0,2)$. Our method is by two measure decompositions, one step…
We introduce and study here a renewal process defined by means of a time-fractional relaxation equation with derivative order $\alpha(t)$ varying with time $t\geq0$. In particular, we use the operator introduced by Scarpi in the Seventies…
Assuming that both a function and its Fourier transform are dominated by a Gaussian of large variance, it is shown that the Hermite coefficients of the function decay exponentially. A sharp estimate for the rate of exponential decay is…
Let A be a set of positive integers with gcd(A) = 1, and let p_A(n) be the partition function of A. Let c = \pi \sqrt(2/3). Let \alpha > 0. It is proved that log p_A(n) ~ c\sqrt(\alpha n) if and only if the set A has asymptotic density…
Consider a supercritical branching random walk on the real line. The consistent maximal displacement is the smallest of the distances between the trajectories followed by individuals at the $n$th generation and the boundary of the process.…
If the inter-arrival time distribution of a renewal process is regularly varying with index $\alpha\in\left( 0,1\right) $ (i.e. the inter-arrival times have infinite mean) and if $A\left( t\right) $ is the associated age process at time…
We give a solution stated in the title to problem 3 of part 1 of the problems listed in the book of Eklof and Mekler [EM],(p.453). There, in pp. 241-242, this is discussed and proved in some cases. The existence of strongly lambda-free ones…
We consider the exponential functional $A_{\infty}=\int_0^{\infty} e^{\xi_s} ds$ associated to a Levy process $(\xi_t)_{t \geq 0}$. We find the asymptotic behavior of the tail of this random variable, under some assumptions on the process…
In this work we establish some rigidity results for Serrin's overdetermined problem \begin{equation*} \left\{ \begin{array}{cll} - \Delta u=f(u) & \text{in}& \Omega,\newline u > 0& \text{in} & \Omega,\newline u=0 & \text{on} & \partial…
In this paper we study the notion of strong non-reflection, and its contrapositive weak reflection. We say theta strongly non-reflects at lambda iff there is a function F: theta ---> lambda such that for all alpha < theta with cf(alpha)=…
We give some general criteria, when kappa-complete forcing preserves largeness properties -- like kappa-presaturation of normal ideals on lambda (even when they concentrate on small cofinalities). Then we quite accurately obtain the…
We generalize the random graph evolution process of Bohman, Frieze, and Wormald [T. Bohman, A. Frieze, and N. C. Wormald, Random Struct. Algorithms, 25, 432 (2004)]. Potential edges, sampled uniformly at random from the complete graph, are…
In neuroscience, the time elapsed since the last discharge has been used to predict the probability of the next discharge. Such predictions can be improved taking into account the last two discharge times, and possibly more. Such multi-time…