Cai, Xing Shi Holmgren, Cecilia

In our previous work [2, 3], we introduced the random k-cut number for rooted graphs. In this paper, we show that the distribution of the k-cut number in complete binary trees of size n, after rescaling, is asymptotically a periodic function of lg n - lg lg n. Thus there are different limit distributions for different subsequences, where these limi...

Lifshits, M. A. Nikitin, Ya. Yu. Petrov, V. V. Zaitsev, A. Yu. Zinger, A. A.
Published in
Vestnik St. Petersburg University, Mathematics

This is the first in a series of reviews devoted to the scientific achievements of the Leningrad–St. Petersburg school of probability and statistics in the period from 1947 to 2017. It is devoted to limit theorems for sums of independent random variables—a traditional subject for St. Petersburg. It refers to the classical limit theorems: the law of...

中村, 隆

"Various aspects of multiple zeta values". July 23～26, 2013. edited by Kentaro Ihara. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / This article is a survey on [1] and [11]. In [1], we give a not infinitely divisible but quasi-infinitely divisible characteristic function on R2. In [11], we give a q...

Glaser, Sven

In this article we deduce a distributional theorem for the realized power variation of linear fractional stable motions. This theorem is proven by choosing the technique of subordination to reduce the proof to a Gaussian limit theorem based on Malliavin-calculus.

Glaser, Sven

We prove a law of large numbers for the power variation of an integrated fractional process in a pure jump model. This yields consistency of an estimator for the integrated volatility where we are no longer restricted to a Gaussian model.

AOYAMA, Takahiro NAKAMURA, Takashi

Kruglov, Victor M.
Published in
Sankhya A

A characterization of the convolution of Gaussian and Poisson laws in the set of infinitely divisible distributions is provided.

Watanabe, Toshiro Yamamuro, Kouji 渡部, 敏郎 山室, 考司

Compound distributions appear in applications to queueing theory and to risk theory. A local property of those distributions on the real line is discussed. The result helps to derive equivalnce conditions to be local subexponential for infinitely divisible distributions on the real line.

Benaych-Georges, Florent

In a previous paper (called "Rectangular random matrices. Related covolution"), we defined, for $\lambda \in [0,1]$, the rectangular free convolution with ratio $\lambda$. Here, we investigate the related notion of infinite divisiblity, which happens to be closely related to the classical infinite divisibility: there exists a bijection between the ...

Lacaux, Céline
Published in
Journal of Theoretical Probability

The asymptotic self-similarity property describes the local structure of a random field. In this paper, we introduce a locally asymptotically self-similar second order field XH,β whose local structures at x=0 and at x≠0 are very far from each other. More precisely, whereas its tangent field at x≠0 is a Fractional Brownian Motion, its tangent field ...