Related papers: A Note on Conditional Expectation for Markov Kerne…
The main goal of this paper is to discuss several approaches to formulation of distributionally robust counterparts of Markov Decision Processes, where the transition kernels are not specified exactly but rather are assumed to be elements…
In this paper, we present a statistical framework for modeling conditional quantiles of spatial processes assumed to be strongly mixing in space. We establish the $L_1$ consistency and the asymptotic normality of the kernel conditional…
Specific matrix elements of exchange and correlation kernels in time-dependent density-functional theory are computed. The knowledge of these matrix elements not only constraints approximate time-dependent functionals, but also allows to…
This paper studies random operator-valued positive definite (p.d.) kernels and their connection to moment dilations. A class of random p.d. kernels is introduced in which the positivity requirement is imposed only in expectation, extending…
Behavioural metrics have been shown to be an effective mechanism for constructing representations in reinforcement learning. We present a novel perspective on behavioural metrics for Markov decision processes via the use of positive…
This work presents a conceptual synthesis of causal discovery and inference frameworks, with a focus on how foundational assumptions -- causal sufficiency, causal faithfulness, and the causal Markov condition -- are formalized and…
We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…
A novel strategy that combines a given collection of $\pi$-reversible Markov kernels is proposed. At each Markov transition, one of the available kernels is selected via a state-dependent probability distribution. In contrast to random-scan…
The classical approach to multivariate extreme value modelling assumes that the joint distribution belongs to a multivariate domain of attraction. This requires each marginal distribution be individually attracted to a univariate extreme…
The standard definition of pedestrian density produces scattered values, hence, many approaches have been developed to improve the features of the estimated density. This paper provides a review of generally applied methods and presents a…
Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of…
For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…
Positive semi-definite kernels are used to induce pseudo-metrics, or ``distances'', between measures. We write these as an expected quadratic variation of, or expected inner product between, a random field and the difference of measures.…
Let $P$ be a Markov kernel on a measurable space $\X$ and let $V:\X\r[1,+\infty)$. We provide various assumptions, based on drift conditions, under which $P$ is quasi-compact on the weighted-supremum Banach space $(\cB_V,\|\cdot\|_V)$ of…
Sublinear expectations for uncertain processes have received a lot of attention recently, particularly methods to extend a downward-continuous sublinear expectation on the bounded finitary functions to one on the non-finitary functions. In…
The solution to a multivariate linear Stochastic Differential Equation (SDE) with constant initial state is well known to be a Gaussian Markov process, but its covariance kernel involves the solution to an integral equation in the general…
In this note, we present few examples of Piecewise Deterministic Markov Processes and their long time behavior. They share two important features: they are related to concrete models (in biology, networks, chemistry,. . .) and they are…
Standard formulations of supervenience typically treat higher level properties as point valued facts strictly fixed by underlying base states. However, in many scientific domains, from statistical mechanics to machine learning, basal…
For a Pfaffian point process we show that its Palm measures, its normalised compositions with multiplicative functionals, and its conditional measures with respect to fixing the configuration in a bounded subset are Pfaffian point processes…
We introduce a new strategy for compositional neural surrogates for radiation-matter interactions, a key task spanning domains from particle physics through nuclear and space engineering to medical physics. Exploiting the locality and the…