Related papers: Weak convergence to extremal processes and record …
We study the convergence of the weak solution of the porous medium equation with a type of Robin boundary conditions, by tuning a parameter either to zero or to infinity. The convergence is in the strong sense, with respect to the…
A weak measurement on a system is made by coupling a pointer weakly to the system and then measuring the position of the pointer. If the initial wavefunction for the pointer is real, the mean displacement of the pointer is proportional to…
We investigate maxima of linear processes with i.i.d. heavy-tailed innovations and random coefficients. Using the point process approach we derive functional convergence of the partial maxima stochastic process in the space of…
A functional limit theorem for the partial maxima of a long memory stable sequence produces a limiting process that can be described as a $\beta$-power time change in the classical Fr\'echet extremal process, for $\beta$ in a subinterval of…
Let $(\xi_1,\eta_1)$, $(\xi_2,\eta_2),\ldots$ be a sequence of i.i.d. two-dimensional random vectors. In the earlier article Iksanov and Pilipenko (2014) weak convergence in the $J_1$-topology on the Skorokhod space of…
First, sufficient conditions are given for a triangular array of random vectors such that the sequence of related random step functions converges towards a (not necessarily time homogeneous) diffusion process. These conditions are weaker…
We prove a sufficient set of conditions for a sequence of finite measures on the space of cadlag measure-valued paths to converge to the canonical measure of super-Brownian motion in the sense of convergence of finite-dimensional…
Based on a weak convergence argument, we provide a necessary and sufficient condition that guarantees that a nonnegative local martingale is indeed a martingale. Typically, conditions of this sort are expressed in terms of integrability…
We consider the behavior of extremal particles in $K$-symmetric exclusion on $\mathbb{Z}$ when the process starts from certain infinite-particle step configurations where there are no particles to the right of a maximal one. In such a…
(English) This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in $\mathbb{R}^k$. In some places, a more general formulation in metric spaces is provided. It lays out the necessary…
We offer an umbrella type result which extends weak convergence of the classical empirical process on the line to that of more general processes indexed by functions of bounded variation. This extension is not contingent on the type of…
The theory of regular model sets is highly developed, but does not cover examples such as the visible lattice points, the k-th power-free integers, or related systems. They belong to the class of weak model sets, where the window may have a…
A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic…
The study of time-inhomogeneous Markov jump processes is a traditional topic within probability theory that has recently attracted substantial attention in various applications. However, their flexibility also incurs a substantial…
Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…
Many environmental processes exhibit weakening spatial dependence as events become more extreme. Well-known limiting models, such as max-stable or generalized Pareto processes, cannot capture this, which can lead to a preference for models…
We investigate the existence of weak solutions to a certain system of partial differential equations, modelling the behaviour of a compressible non-Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
We investigate the impact of dissipation on weak measurements. While weak measurements have been successful in signal amplification, dissipation can compromise their usefulness. More precisely, we show that in systems with non-degenerate…
Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes simulation highly nontrivial. Algorithms based on finite…