相关论文: The strong renewal theorem with infinite mean via …
It is well known that a continuously differentiable function is monotone in an interval $[a,b]$ if and only if its first derivative does not change its sign there. We prove that this is equivalent to requiring that the Caputo derivatives of…
The seminal theorem of Cobham has given rise during the last 40 years to a lot of works around non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a…
Finding necessary and sufficient conditions for isomorphism between two semigroups of order-preserving transformations over an infinite domain with restricted range was an open problem in \cite{FHQS}. In this paper, we show a proof strategy…
The asymptotic study of a time-dependent function $f$ as the solution of a differential equation often leads to the question of whether its derivative $\dot f$ vanishes at infinity. We show that a necessary and sufficient condition for this…
In this paper, we consider inverse limits of $[0,1]$ using upper semicontinuous set-valued functions. We aim to expand on a previous paper exploring the relationship between the existence periodic points of a continuous function to the…
If $X$ is a spectrally positive stable process of index $\alpha\in(1,2)$ whose L\'{e}vy measure has density $cx^{-\alpha-1}$ on $(0,\infty),$ and $S_1=\sup_{0<t\leq1}X_t,$ it is known that $P(S_1>x)\backsim c\alpha^{-1}x^{-\alpha}$ as…
Caputo fractional (with power-law kernels) and fractional (delta) difference maps belong to a more widely defined class of generalized fractional maps, which are discrete convolutions with some power-law-like functions. The conditions of…
We give another proof that for every lambda >= beth_omega for every large enough regular kappa < beth_omega we have lambda^{[kappa]}= lambda, dealing with sufficient conditions for replacing beth_omega by aleph_omega. In section 2 we show…
For near-critical, transient Markov chains on the non-negative integers in the Lamperti regime, where the mean drift at $x$ decays as $1/x$ as $x \to \infty$, we quantify degree of transience via existence of moments for conditional return…
In this short note we prove that, if (C[a,b],{A_n}) is an approximation scheme and (A_n) satisfies de La Vall\'ee-Poussin Theorem, there are instances of continuous functions on [a,b], real analytic on (a,b], which are poorly approximable…
Consider a spectrally positive L\'evy process $Z$ with log-Laplace exponent $\Psi$ and a positive continuous function $R$ on $(0,\infty)$. We investigate the entrance from $\infty$ of the process $X$ obtained by changing time in $Z$ with…
We derive equivalent conditions for the (local) absolute continuity of two laws of semimartingales on random sets. Our result generalizes previous results for classical semimartingales by replacing a strong uniqueness assumption by a weaker…
The goal of this note is to provide an alternative proof of Theorem 1.1 (i) in [4], that is, if $n\geq 2$ and $M^{\alpha}$ is bounded on $L^{p}(\mathbb{R}^{n})$ for some $\alpha\in \mathbb{C}$ and $p\geq 2$, then we have \begin{align*}…
We prove a probabilistic Fourier extension theorem that says Fourier extension holds when averaged over certain smooth Alpert multipliers. The proofs use smooth Alpert wavelets with the classical techniques of stationary phase and…
Any renewal processes on $\mathbb{N}$ with a polynomial tail, with exponent $\alpha \in (0,1)$, has a non-trivial scaling limit, known as the $\alpha$-stable regenerative set. In this paper we consider Gibbs transformations of such renewal…
We show that the porous medium equation does not in general preserve $\alpha$-concavity of the pressure for $0\le\alpha<1/2$ or $1/2<\alpha\le 1$. In particular, this resolves an open problem of V\'azquez on whether concavity of pressure is…
Suppose that i.i.d. random variables $X_{1}, X_{2}, \ldots$ are chosen uniformly from $[0,1]$, and let $f: [0,1] \rightarrow [0,1]$ be an increasing bijection. Define $\mu_{f}$ to be the expected value of $f(X_{i})$ for each $i$. Define the…
We revisit processes generated by iterated random functions driven by a stationary and ergodic sequence. Such a process is called strongly stable if a random initialization exists, for which the process is stationary and ergodic, and for…
We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…
We study an extension of the sandwiched R\'enyi relative entropies for normal positive functionals on a von Neumann algebra, for parameter values $\alpha\in [1/2,1)$. This work is intended as a continuation of [A. Jen\v{c}ov\'a, Ann. Henri…