Related papers: Conditional measures for Pfaffian point processes:…
We characterize the condition $(\Omega)$ for smooth kernels of partial differential operators in terms of the existence of shifted fundamental solutions satisfying certain properties. The conditions $(P\Omega)$ and…
The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…
We study the topological complexity of sets defined using Khovanskii's Pfaffian functions, in terms of an appropriate notion of format for those sets. We consider semi- and sub-Pfaffian sets, but more generally any definable set in the…
Spatial Poisson point processes on finite-dimensional Euclidean space provide fundamental mathematical tools for modeling random spatial point patterns. In this paper, we introduce and analyze several Poisson-type spatial point processes.…
Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…
We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
We develop a theory of insertion and deletion tolerance for point processes. A process is insertion-tolerant if adding a suitably chosen random point results in a point process that is absolutely continuous in law with respect to the…
The potential applications of boundary functionals of random processes, such as the extreme values of these processes, the moment of first reaching a fixed level, the value of the process at the moment of reaching the level, the moment of…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless…
Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for…
We define multideterminantal probability measures, a family of probability measures on $[k]^n$ where $[k]=\{1,2,\dots,k\}$, generalizing determinantal measures (which correspond to the case $k=2$). We give examples coming from the positive…
In this paper we consider spatial processes and measure dynamical systems over locally compact Abelian groups. We characterize when a spatial processes is equivalent to a translation bounded measure dynamical systems and we characterize…
In the paper a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems the constraints depend both on the parameter as well as on the decision variable itself and they…
We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is…
Coalescing particles on a line merge when they meet. As they do, their basins of attraction merge and the walls between basins disappear. If every site is initially occupied, these walls at any positive time form a Pfaffian point process:…
We present axiomatisations for a number of partial function signatures that include domain restriction, modelled as a right normal band operation. Other operations considered are override and update, difference, minus, intersection,…
We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and…
Under certain mild conditions, limit theorems for additive functionals of some $d$-dimensional self-similar Gaussian processes are obtained. These limit theorems work for general Gaussian processes including fractional Brownian motions,…