Related papers: Quantitative exponential bounds for the renewal th…
Chernoff approximations to strongly continuous one-parameter semigroups give solutions to a wide class of differential equations. This paper studies the rate of convergence of the Chernoff approximations. We provide simple natural examples…
We prove the existence and uniqueness of measure solutions to the conservative renewal equation and analyze their long time behavior. The solutions are built by using a duality approach. This construction is well suited to apply the…
Exchangeability -- in which the distribution of an infinite sequence is invariant to reorderings of its elements -- implies the existence of a simple conditional independence structure that may be leveraged in the design of statistical…
Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of…
The aim of this work is to illustrate a conditional result involving the exponential sums over primes in short intervals under the assumption that both the Generalized Riemann Hypothesis and the Density Hypothesis for Dirichlet…
We derive continuous dependence estimates for weak entropy solutions of degenerate parabolic equations with nonlinear fractional diffusion. The diffusion term involves the fractional Laplace operator, $\Delta^{\alpha/2}$ for $\alpha \in…
We construct a one-dimensional piecewise linear intermittent map from the interevent time distribution for a given renewal process. Then, we characterize intermittency by the asymptotic behavior near the indifferent fixed point in the…
This work deals with the large time behaviour of the spatially homogeneous Landau equation with Coulomb potential. Firstly, we obtain a bound from below of the entropy dissipation $D(f)$ by a weighted relative Fisher information of $f$ with…
Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia,…
Some results on cross-diffusion systems with entropy structure are reviewed. The focus is on local-in-time existence results for general systems with normally elliptic diffusion operators, due to Amann, and global-in-time existence theorems…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
We give a simple statistical proof of a binomial identity, by evaluating the Laplace transform of the maximum of n independent exponential random variables in two different ways. As a by product, we obtain a simple proof of an interesting…
Renewal theory is finding increasing applications in non-equilibrium statistical physics. One example relates the probability density and survival probability of a Brownian particle or an active run-and-tumble particle with stochastic…
We study exponential stability for a kind of neural networks having time-varying delay. By extending the auxiliary function-based integral inequality, a novel integral inequality is derived by using weighted orthogonal functions of which…
We derive the exponential non improvable Grand Lebesgue Space norm decreasing estimations for tail of distribution for exact normed deviation for the famous recursive Wolverton-Wagner multivariate statistical density estimation. We consider…
We study the top Lyapunov exponent of a product of random $2 \times 2$ matrices appearing in the analysis of several statistical mechanical models with disorder, extending a previous treatment of the critical case (Giacomin and Greenblatt,…
We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and…
We consider a system of reaction-diffusion equations describing the reversible reaction of two species $\mathcal{U}, \mathcal{V}$ forming a third species $\mathcal{W}$ and vice versa according to mass action law kinetics with arbitrary…
We establish an exponential error term for the renewal theorem in the context of products of random matrices, which is surprising compared with classical abelian cases. A key tool is the Fourier decay of the Furstenberg measures on the…
We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the…