The frequency stability of an optical frequency standard at 729 nm, based on a single
calcium ion, is numerically studied. It is investigated through the Allan deviation, whose …

We consider the pricing of life insurance contracts under stochastic mortality and interest
rates assumed not independent of each other. Employing the method of change of measure …

We adapt ideas and concepts developed in optimal transport (and its martingale variant) to
give a geometric description of optimal stopping times τ τ of Brownian motion subject to the …

From both theoretical and applied perspectives, first passage time problems for random
processes are challenging and of great interest. In this thesis, our contribution consists on …

Classical contact geometry is an odd-dimensional analogue of symplectic geometry. We
show that a natural probabilistic deformation of contact geometry, compatible with the very …

Firstly, we compute the distribution function for the hitting time of a linear time-dependent
boundary t↦ a+ bt, a≥ 0, b∈ ℝ, by a reflecting Brownian motion. The main tool hereby is …

We review and study a one-parameter family of functional transformations, denoted by (S
(β)) β∈ ℝ, which, in the case β< 0, provides a path realization of bridges associated to the …

Sharp maximal inequalities in large and small range are derived for stable stochastic
integrals. In order to control the tail of a stable process, we introduce a truncation level in the …

The first passage time problem for Brownian motions hitting a barrier has been extensively
studied in the literature. In particular, many incarnations of integral equations which link the …

In this paper we consider a connection between the famous Skorokhod embedding problem
and the Shiryaev inverse problem for the first hitting time distribution of a Brownian motion …