No abstract available

[en] We reply to the comments of Greczylo and Debowsca and offer additional suggestions on performing experiments to measure Brownian motion. (letters and comments)

[en] In 2003 Lawler and Werner introduced the Brownian loop measure and studied some of its properties. In 2006 Cardy and Gamsa predicted a formula for the total mass that the Brownian loop measure assigns to the set of simple loops in the upper half plane disconnecting two given points from the boundary. In this paper we give a rigorous proof of this formula. Moreover, we present several applications of the formula to conformal restriction measures and CLE.

[en] We derive the moments of the first passage time for Brownian motion conditioned by either the maximum value or the area swept out by the motion. These quantities are the natural counterparts to the moments of the maximum value and area of Brownian excursions of fixed duration, which we also derive for completeness within the same mathematical framework. Various applications are indicated. (paper)

[en] Highlights: • Detection of coherent sets in evolving particle ensembles without underlying flow map. • Connection of Frobenius–Perron operator theory and regularized optimal transport (OT). • Motivation for regularized OT along Schrödinger’s question from statistical physics. • Creation and destruction of mass within coherent sets using unbalanced OT. • Various interesting proof-of-the-concept examples. The topic of this study lies in the intersection of two fields. One is related with analyzing transport phenomena in complicated flows. For this purpose, we use so-called coherent sets: non-dispersing, possibly moving regions in the flow’s domain. The other is concerned with reconstructing a flow field from observations of its action on a measure, which we address by optimal transport. We show that the framework of optimal transport is well suited for delivering the formal requirements on which a coherent-set analysis can be based on. The necessary noise-robustness requirement of coherence can be matched by the computationally efficient concept of unbalanced regularized optimal transport. Moreover, the applied regularization can be interpreted as an optimal way of retrieving the full dynamics given the extremely restricted information of an initial and a final particle distribution moving according to Brownian motion.

No abstract available

[en] Open quantum walks (OQWs) are a class of quantum walks, which are purely driven by the interaction with the dissipative environment. In this paper, we review theoretical advances on the foundations of discrete time OQWs, continuous time OQWs and a scaling limit of OQWs called open quantum Brownian motion. The main focus of the review is on the results and developments of discrete time OQW, covering general formalism, quantum trajectories for OQWs, central limit theorems, the microscopic derivation as well as possible generalisations and applications of OQWs.

[en] We present new algorithms for simulation of fractional Brownian motion (fBm) which comprises a set of important random functions widely used in geophysical and physical modeling, fractal image (landscape) simulating, and signal processing. The new algorithms, which are both accurate and efficient, allow us to generate not only a one-dimensional fBm process, but also two- and three-dimensional fBm fields. 23 refs., 3 figs

[en] An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The analysis leads to a simple closed-form solution for the moments of the Airy distribution. (fast track communication)

[en] By using stochastic analysis, fractional analysis, compact semigroups and the Schauder fixed-point theorem, we discuss the approximate boundary controllability of a nonlocal Hilfer fractional stochastic differential system with fractional Brownian motion and a Poisson jump. In addition, we establish the sufficient conditions for exact null controllability for the same problem. Finally, an example is given to illustrate the results obtained.