相关论文: Effective computations of joint excursion times fo…

Relying on the excursion set theory, we compute the number density of local extrema and crossing statistics versus the threshold for the stock market indices. Comparing the number density of excursion sets calculated numerically with the…

Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…

S. G. Kou and H. Wang [First Passage times of a Jump Diffusion Process \textit{Ann. Appl. Probab.} {\bf 35} (2003) 504--531] give expressions of both the (real) Laplace transform of the distribution of first passage time and the (real)…

We develop importance sampling based efficient simulation techniques for three commonly encountered rare event probabilities associated with random walks having i.i.d. regularly varying increments; namely, 1) the large deviation…

Insight into a number of interesting questions in cosmology can be obtained from the first crossing distributions of physically motivated barriers by random walks with correlated steps. We write the first crossing distribution as a formal…

We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…

Missing observations are pervasive throughout empirical research, especially in the social sciences. Despite multiple approaches to dealing adequately with missing data, many scholars still fail to address this vital issue. In this paper,…

The study of multimodality has garnered significant interest in fields where the analysis of interactions among multiple information sources can enhance predictive modeling, data fusion, and interpretability. Partial information…

The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in $n$ fixed points at $n$ fixed past instants. In particular, functional large deviation results are stated for small time. Several…

We introduce an effective algorithmic method for the computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach employs interval arithmetic and thus provides a rigorous numerical result (computer-assisted…

We investigate the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain. The encounters with each subset are characterized by the boundary local time on that subset. We extend a…

Established techniques for simulation and prediction with Gaussian process (GP) dynamics often implicitly make use of an independence assumption on successive function evaluations of the dynamics model. This can result in significant error…

By using the matrix formulation of the two-step approach to the distributions of runs, a recursive relation and an explicit expression are derived for the generating function of the joint distribution of rises and falls for multivariate…

In this paper, we provide faster algorithms for computing various fundamental quantities associated with random walks on a directed graph, including the stationary distribution, personalized PageRank vectors, hitting times, and escape…

The excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the dark matter halo mass function. The computation of the mass function is mapped into the so-called…

We address the challenge of lifting 2D visual segmentation to 3D in Gaussian Splatting. Existing methods often suffer from inconsistent 2D masks across viewpoints and produce noisy segmentation boundaries as they neglect these semantic cues…

Recently, there has been growing interest in developing optimization methods for solving large-scale machine learning problems. Most of these problems boil down to the problem of minimizing an average of a finite set of smooth and strongly…

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 consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…

This paper presents the design of a novel distributed algorithm d-IRA for the reachability analysis of linear hybrid automata. Recent work on iterative relaxation abstraction (IRA) is leveraged to distribute the computational problem among…