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We correct two errors of omission in our paper, On Levy processes conditioned to stay positive. Electron. J. Probab. 10, (2005), no. 28, 948--961. Math. Review 2006h:60079.

It is shown that the usual method of establishing Cramer's estimate also works for Levy processes.

We obtain a new fluctuation identity for a general Levy process giving a quintuple law describing the time of first passage, the time of the last maximum before first passage, the overshoot, the… (More)

- Ronald A. Doney
- 1997

Summary. If {Sn,n≧0} is an integer-valued random walk such that Sn/an converges in distribution to a stable law of index α∈ (0,1) as n→∞, then Gnedenko’s local limit theorem provides a useful… (More)

- Ronald A. Doney
- 2007

Recently there has been renewed interest in fluctuation theory for Levy processes. Inthis brief survey we describe several aspects of this topic, including Wiener-Hopf factorisation,the ladder… (More)

Let S be a real-valued random walk that does not drift to ∞, so P(S k ≥ 0 for all k)=0. We condition S to exceed n before hitting the negative halfline, respectively, to stay nonnegative up to time… (More)

- Ronald A. Doney
- 1985

We prove some limiting results for a Lévy process Xt as t↓0 or t→∞, with a view to their ultimate application in boundary crossing problems for continuous time processes. In the present paper we are… (More)

Abstract. Any solution of the functional equation
where B is a Brownian motion, behaves like a reflected Brownian motion, except when it attains a new maximum: we call it an α-perturbed reflected… (More)

We prove that when a sequence of Levy processes X (n) or a normed sequence of random walks S (n) converges a.s. on the Skorokhod space toward a Levy process X, the sequence L (n) of local times at… (More)