Related papers: Conditional measures for Pfaffian point processes:…
There has been significant developments in the classification of boundary conditions of positive symmetric systems, also known as Friedrichs systems, after the introduction of operator theoretic framework. We take a step forward towards…
The asymptotic behaviour of empirical measures has been studied extensively. In this paper, we consider empirical measures of given subordinated processes on complete (not necessarily compact) and connected Riemannian manifolds with…
Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…
The propositional planning problem is a notoriously difficult computational problem. Downey et al. (1999) initiated the parameterized analysis of planning (with plan length as the parameter) and B\"ackstr\"om et al. (2012) picked up this…
A point process is said to be rigid if for any bounded domain in the phase space, the number of particles in the domain is almost surely determined by the restriction of the configuration to the complement of our bounded domain. The main…
Measurements are shown to be processes designed to return figures: they are effective. This effectivity allows for a formalization as Turing machines, which can be described employing computation theory. Inspired in the halting problem we…
Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…
A Hawkes process on $\R$ is a point process whose intensity function at time $t$ is a functional of its past activity before time $t$. It is defined by its activation function $\Phi$ and its memory function $h$. In this paper, the Hawkes…
Estimating causal quantities traditionally relies on bespoke estimators tailored to specific assumptions. Recently proposed Causal Foundation Models (CFMs) promise a more unified approach by amortising causal discovery and inference in a…
Let X be a locally compact Polish space and let m be a reference Radon measure on X. Let $\Gamma_X$ denote the configuration space over X, that is, the space of all locally finite subsets of X. A point process on X is a probability measure…
We extend Monte Carlo samplers based on piecewise deterministic Markov processes (PDMP samplers) by formally defining different boundary conditions such as sticky floors, soft and hard walls and teleportation portals. This allows PDMP…
We prove existence of boundary limits of ratios of positive harmonic functions for a wide class of Markov processes with jumps and irregular domains, in the context of general metric measure spaces. As a corollary, we prove uniqueness of…
Kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same…
We formalize algorithms computing Pfaffian in the theory of bounded arithmetic for sharpL which is based on Berkowitz algorithm for the determinant. We also prove relations among Pfaffian properties. Furthermore, we give an algorithm for…
For characterizing the Brownian motion in a bounded domain: $\Omega$, it is well-known that the boundary conditions of the classical diffusion equation just rely on the given information of the solution along the boundary of a domain; on…
We discuss the practice of directly or indirectly assuming a model for the number of points when modelling spatial point patterns even though it is rarely possible to validate such a model in practice since most point pattern data consist…
In this paper we present some bounds of Hausdorff measures of objects definable in o-minimal structures: sets, fibers of maps, inverse images of curves of maps, etc. Moreover, we also give some explicit bounds for semi-algebraic or…
Fractional Brownian motion can be represented as an integral of a deterministic kernel w.r.t. an ordinary Brownian motion either on infinite or compact interval. In previous literature fractional L\'evy processes are defined by integrating…