arXiv subjects

Péter Kevei

Publications and source records attributed to Péter Kevei.

24 records · Page 2Linked to original sources

arXiv2014

The limit distribution of ratios of jumps and sums of jumps of subordinators

Let $V_{t}$ be a driftless subordinator, and let denote $m_{t}^{(1)} \geq m_{t}^{(2)} \geq\ldots$ its jump sequence on interval $[0,t]$. Put $V_{t}^{(k)} = V_{t} - m_{t}^{(1)} - \ldots- m_{t}^{(k)}$ for the $k$-trimmed subordinator. In this note we characterize under what conditions the limiting distribution of the ratios $V_{t}^{(k)} / m_{t}^{(k+1)}$ and $m_{t}^{(k+1)} / m_{t}^{(k)}$ exist, as $t \downarrow0$ or $t \to\infty$.

math.PR↗

arXiv2014

On the diminishing process of B. Tóth

Let $K$ and $K_0$ be convex bodies in $\mathbb{R}^d$, such that $K$ contains the origin, and define the process $(K_n, p_n)$, $n \geq 0$, as follows: let $p_{n+1}$ be a uniform random point in $K_n$, and set $K_{n+1} = K_n \cap (p_{n+1} + K)$. Clearly, $(K_n)$ is a nested sequence of convex bodies which converge to a non-empty limit object, again a convex body in $\mathbb{R}^d$. We study this process for $K$ being a regular simplex, a cube, or a regular convex polygon with an odd number of vertices. We also derive some new results in one dimension for non-uniform distributions.

math.PR↗

arXiv2013

Asymptotic behavior of a multi-type nearly critical Galton--Watson processes with immigration

Multi-type inhomogeneous Galton--Watson process with immigration is investigated, where the offspring mean matrix slowly converges to a critical mean matrix. Under general conditions we obtain limit distribution for the process, where the coordinates of the limit vector are not necessarily independent.

math.PR↗

arXiv2013

A More General Maximal Bernstein-type Inequality

We extend a general Bernstein-type maximal inequality of Kevei and Mason (2011) for sums of random variables.

math.PR↗

arXiv2011

The diminishing segment process

Let S(1) be the segment [-1,1], and define the segments S(n) recursively in the following manner: let S(n+1) be the intersection of S(n) and a(n+1) + S(1), where the point a(n+1) is chosen randomly on the segment S(n) with uniform distribution. For the radius r(n) of S(n) we prove that n(r(n) - 1//2) converges in distribution to an exponential law, and we also show that the centre of the limiting unit interval has arcsine distribution.

math.PR↗

arXiv2011

A note on a maximal Bernstein inequality

We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.

math.ST↗