Point processes often have a natural interpretation with respect to a continuous process. We
propose a point process construction that describes arrival time observations in terms of the …

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 …

We prove existence and uniqueness for the inverse-first-passage time problem for soft-killed
Brownian motion using rather elementary methods relying on basic results from probability …

▶ Existence and uniqueness for ξ with no atoms (Chen, Cheng, et al. 2011, free boundary
problem)▶ Uniqueness (Ekström and Janson 2016, optimal stopping problem, see also …

Given a distribution on the positive extended real line, the two-sided inverse first-passage
time problem for Brownian motion asks for a function such that the first passage time of this …

Пусть задано распределение на расширенной положительной оси; двусторонняя
обратная задача о моменте первого пересечения для броуновского движения …

We revisit an inverse first-passage time (IFPT) problem, in the cases of fractional Brownian
motion, and time-changed Brownian motion. Let X (t) be a one dimensional continuous …

The theoretical description of nonrenewal stochastic systems is a challenge. Analytical
results are often not available or can be obtained only under strong conditions, limiting their …

Let X (t) be a continuously time-changed Brownian motion starting from a random position η,
S (t) a given continuous, increasing boundary, with S (0)≥ 0, P (η≥ S (0))= 1, and F an …

This thesis deals with different formulations and views of distribution-constrained
optimization problems. One of them is a classical optimal stopping problem with additional …