This paper concerns a recurrent random walk on the real line and obtains a purely analytic result concerning the characteristic function, which is useful for dealing with some problems of probabilistic interest for the walk of infinite variance: it reduces them to the case when the increment...

We develop criteria for recurrence and transience of one-dimensional Markov processes which have jumps and oscillate between +[infinity] and -[infinity]. The conditions are based on a Markov chain which only consists of jumps (overshoots) of the process into complementary parts of the state...

We show that an isotropic self-similar Markov process in has a skew product structure if and only if its radial and angular parts do not jump at the same time.

The purpose of this note is to correct an error in Baltrunas et al. (2004) [1], and to give a more detailed argument to a formula whose validity has been questioned over the years. These details close a gap in the proof of Theorem 4.1 as originally stated, the validity of which is...

We investigate the behaviour of a chain of interacting Brownian particles with one end fixed and the other end moving away at slow speed [epsilon]0, in the limit of small noise. The interaction between particles is through a pairwise potential U with finite range b0. We consider both overdamped...

We construct a stochastic calculus with respect to the local time process of a symmetric Lévy process X without Brownian component. The required assumptions on the Lévy process are satisfied by the symmetric stable processes with index in (1,2). Based on this construction, the explicit...

We consider a branching random walk on starting from x=0 and with a killing barrier at 0. At each step, particles give birth to b children, which move independently. Particles that enter the negative half-line are killed. In the case of almost sure extinction, we find asymptotics for the...

We study the extremes of a sequence of random variables (Rn) defined by the recurrence Rn=MnRn-1+q, n=1, where R0 is arbitrary, (Mn) are iid copies of a non-degenerate random variable M, 0<=M<=1, and q>0 is a constant. We show that under mild and natural conditions on M the suitably normalized extremes of...</=m<=1,>

We investigate large deviations for the empirical measure of the forward and backward recurrence time processes associated with a classical renewal process with arbitrary waiting-time distribution. The Donsker-Varadhan theory cannot be applied in this case, and indeed it turns out that the large...

An asymptotic distribution theory of the nonsynchronous covariation process for continuous semimartingales is presented. Two continuous semimartingales are sampled at stopping times in a nonsynchronous manner. Those sampling times possibly depend on the history of the stochastic processes and...