Zobrazeno 1 - 10
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pro vyhledávání: '"Doney, Ron A."'
Autor:
Doney, Ron
Several terms in an asynptotic estimate for the renewal mass function ina discrete random walk which has positive mean and regularly varying right-hand tail are given. Similar results are given for the renewal density function in the absolutely conti
Externí odkaz:
http://arxiv.org/abs/2301.09593
Autor:
Doney, Ron
If the step distribution in a renewal process has finite mean and regularly varying tail with index -{\alpha}, 1<{\alpha}<2, the first two terms in the asymptotic expansion of the renewal function have been known for many years. Here we show that, wi
Externí odkaz:
http://arxiv.org/abs/1909.11458
Autor:
Chaumont, Loïc, Doney, Ron
According to the Wiener-Hopf factorization, the characteristic function $\varphi$ of any probability distribution $\mu$ on $\mathbb{R}$ can be decomposed in a unique way as \[1-s\varphi(t)=[1-\chi_-(s,it)][1-\chi_+(s,it)]\,,\;\;\;|s|\le1,\,t\in\mathb
Externí odkaz:
http://arxiv.org/abs/1702.00067
Autor:
Caravenna, Francesco, Doney, Ron
Publikováno v:
Electron. J. Probab. 24 (2019), paper no. 72, 1-48
We establish two different, but related results for random walks in the domain of attraction of a stable law of index $\alpha$. The first result is a local large deviation upper bound, valid for $\alpha \in (0,1) \cup (1,2)$, which improves on the cl
Externí odkaz:
http://arxiv.org/abs/1612.07635
Publikováno v:
Bernoulli 2016, Vol. 22, No. 3, 1491-1519
We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case), but possib
Externí odkaz:
http://arxiv.org/abs/1306.1720
Autor:
Doney, Ron A., Vakeroudis, Stavros
Using a generalization of the skew-product representation of planar Brownian motion and the analogue of Spitzer's celebrated asymptotic Theorem for stable processes due to Bertoin and Werner, for which we provide a new easy proof, we obtain some limi
Externí odkaz:
http://arxiv.org/abs/1203.3739
Autor:
Doney, Ron, Korshunov, Dmitry
We consider a transient random walk on $Z^d$ which is asymptotically stable, without centering, in a sense which allows different norming for each component. The paper is devoted to the asymptotics of the probability of the first return to the origin
Externí odkaz:
http://arxiv.org/abs/1104.3191
Autor:
Doney, Ron, Savov, Mladen
Publikováno v:
Annals of Probability 2010, Vol. 38, No. 4, 1390-1400
We call a right-continuous increasing process $K_x$ a partial right inverse (PRI) of a given L\'{e}vy process $X$ if $X_{K_x}=x$ for at least all $x$ in some random interval $[0,\zeta)$ of positive length. In this paper, we give a necessary and suffi
Externí odkaz:
http://arxiv.org/abs/0904.4871
Autor:
Chaumont, Loïc, Doney, Ron Arthur
We prove that when a sequence of L\'evy processes $X^{(n)}$ or a normed sequence of random walks $S^{(n)}$ converges a.s. on the Skorokhod space toward a L\'evy process $X$, the sequence $L^{(n)}$ of local times at the supremum of $X^{(n)}$ converges
Externí odkaz:
http://arxiv.org/abs/0903.3705
Autor:
Doney, Ron, Maller, Ross
Publikováno v:
Annals of Probability 2007, Vol. 35, No. 4, 1351-1373
Let $R_n=\max_{0\leq j\leq n}S_j-S_n$ be a random walk $S_n$ reflected in its maximum. Except in the trivial case when $P(X\ge0)=1$, $R_n$ will pass over a horizontal boundary of any height in a finite time, with probability 1. We extend this by givi
Externí odkaz:
http://arxiv.org/abs/0708.1676