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The Shape Calculus is a bio-inspired calculus for describing 3D shapes moving in a space. A shape forms a 3D process when combined with a behaviour. Behaviours are specified with a timed CCS-like process algebra using a notion of channel…
A Gaussian process has been one of the important approaches for emulating computer simulations. However, the stationarity assumption for a Gaussian process and the intractability for large-scale dataset limit its availability in practice.…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…
In this paper we study the one-sided shift operator on a state space defined by a finite alphabet. Using a scheme developed by Walters [13], we prove that the sequence of iterates of the transfer operator converges under square summability…
Causal reversibility blends reversibility and causality for concurrent systems. It indicates that an action can be undone provided that all of its consequences have been undone already, thus making it possible to bring the system back to a…
In this paper we consider square functions (also called Littlewood-Paley g-functions) associated to Hankel convolutions acting on functions in the Bochner-Lebesgue space $L^p((0,\infty),B)$, where $B$ is a UMD Banach space. As special cases…
This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using…
We define a measure on tuples of partitions, called the symplectic Schur process, that should be regarded as the right analogue of the Schur process of Okounkov-Reshetikhin for the Cartan type C. The weights of our measure include factors…
Time-reversal symmetry is a prevalent feature of microscopic physics, including operational quantum theory and classical general relativity. Previous works have studied indefinite causal structure using the language of operational quantum…
The twisted Gaussian Schell Model describes a family of partially coherent beams that present several interesting characteristics, and as such have attracted attention in classical and quantum optics. Recent techniques have been…
This is a survey of results about permanental processes, real valued positive processes which are a generalization of squares of Gaussian processes. In a certain sense the symmetric positive definite function that determines a Gaussian…
Let B(t), X(t) and Y(t) be independent standard 1d Borwnian motions. Define X^+(t) and Y^-(t) as the trajectories of the processes X(t) and Y(t) pushed upwards and, respectively, downwards by B(t), according to Skorohod-reflection. In a…
In the G-framework, we establish existence of an optimal stochastic relaxed control for stochastic differential equations driven by a G-Brownian motion.
As represented by the Liouville measure, Gaussian multiplicative chaos is a random measure constructed from a Gaussian field. Under certain technical assumptions, we prove the convergence of a process time-changed by Gaussian multiplicative…
In this paper, we first review the penalization method for solving deterministic Skorokhod problems in non-convex domains and establish estimates for problems with $\alpha$-H\"older continuous functions. With the help of these results…
A new high order accurate staggered semi-implicit space-time discontinuous Galerkin (DG) method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions. The staggered DG…
We use the so called resolvent transform method to study the cyclicity of the one point mass singular inner function in weighted Bergman type spaces.