Let X and Y be two independent random walks on with zero mean and finite variances, and let Lt(X,Y) be the local time of X-Y at the origin at time t. We show that almost surely with respect to Y, Lt(X,Y)/logt conditioned on Y converges in distribution to an exponential random variable with the...

Let {Ai} be a sequence of random positive numbers, such that only N first of them are strictly positive, where N is a finite a.s. random number. In this paper we investigate nonnegative solutions of the distributional equation , where Z,Z1,Z2,... are independent and identically distributed...

We study a stochastic particle system which models the time evolution of the ranking of books by online bookstores (e.g., Amazon.co.jp). In this system, particles are lined in a queue. Each particle jumps at random jump times to the top of the queue, and otherwise stays in the queue, being...

We consider optimal stopping problems with finite horizon for one-dimensional diffusions. We assume that the reward function is bounded and Borel-measurable, and we prove that the value function is continuous and can be characterized as the unique solution of a variational inequality in the...

We use Nummelin splitting in continuous time in order to prove laws of iterated logarithm for additive functionals of a Harris recurrent Markov process, with deterministic or random renormalization.

In this paper, the authors firstly construct a graph-theoretic decomposition of an index set for tree martingales, and based on this decomposition, they give a locally finite tree martingale's notion and a tree martingale decomposition theorem. Secondly, they establish some relations between the...

We develop the asymptotic theory for the realised power variation of the processes X=[phi]-G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity conditions on the path of...

Mild sufficient conditions for exponential ergodicity of a Markov process defined as the solution to a SDE with jump noise are given. These conditions include three principal claims: recurrence condition , topological irreducibility condition and non-degeneracy condition , the latter formulated...

We study transport properties of isotropic Brownian flows. Under a transience condition for the two-point motion, we show asymptotic normality of the image of a finite measure under the flow and-under slightly stronger assumptions-asymptotic normality of the distribution of the volume of the...

For observations from an auto-regressive moving-average process on any number of dimensions, we propose a modification of the Gaussian likelihood, which when maximized corrects the edge-effects and fixes the order of the bias for the estimators derived. We show that the new estimators are not...