We give explicit upper bounds for convergence rates when approximating both oneand two-sided general curvilinear boundary crossing probabilities for the Wiener process by similar probabilities for… (More)

We give a new relatively compact proof of the famous identity for the distribution of the first hitting time of a linear boundary by a skip-free process with stationary independent increments. The… (More)

We derive a closed-form (infinite series) representation for the distribution of the ruin time for the Sparre Andersen model with exponentially distributed claims. This extends a recent result of… (More)

We introduce a new class of dynamic point process models with simple and intuitive dynamics that are based on the Voronoi tessellations generated by the processes. Under broad conditions, these… (More)

We prove two martingale identities which involve exit times of Lévy-driven Ornstein–Uhlenbeck processes. Using these identities we find an explicit formula for the Laplace transform of the exit time… (More)

Let X1, . . . ,Xk and Y 1, . . . , Y m be jointly independent copies of random variables X and Y , respectively. For a fixed total number n of random variables, we aim at maximising M(k,m) :=… (More)

We consider a piecewise-deterministic Markov process governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the… (More)