Necessary and Sufficient Conditions for FKG Inequalities in Stochastic Processes
This paper establishes necessary and sufficient conditions for various stochastic processes, including Lévy processes, Bessel processes, and conditioned Brownian processes, to satisfy the FKG inequality, a fundamental correlation inequality in probability theory. The key tool is an approximation of these processes using Markov chains and random walks.
자기분해 가능 극한 법칙의 정량적 일반화에 대한 고찰: 스펙트럼 방법을 이용하여
자기분해 가능 및 비퇴화 대칭 α-안정 확률 측도에 대한 새로운 안정성 추정치를 제시하였다. 이는 Stein 방법과 가중 Poincaré 부등식을 활용하여 얻은 결과이다.
Quantitative Generalized Central Limit Theorems with Self-Decomposable and Symmetric Stable Limiting Laws
This work provides new stability estimates for centered non-degenerate self-decomposable probability measures on Rd with finite second moment and for non-degenerate symmetric α-stable probability measures on Rd with α ∈ (1, 2). The proofs rely on Stein's method, closed forms techniques, and weighted Poincaré-type inequalities. The results yield explicit rates of convergence in Wasserstein-type distances for several instances of generalized central limit theorems.
Tight Nonasymptotic Bounds on Relative Entropy Between Sampling With and Without Replacement
Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of c ≥ 2 colors. The bounds depend on the number of balls of each color in the urn.
Conditioning of Banach Space Valued Gaussian Random Variables: An Approximation Approach Based on Martingales
The core message of this article is to provide a general framework for conditioning one Banach space valued Gaussian random variable with respect to another, including an approximation scheme based on martingales that allows for efficient computation of the conditional means and covariances.
Information Divergences and Likelihood Ratios for Poisson Processes and Point Patterns
This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical formulas for Kullback–Leibler divergences, Rényi divergences, Hellinger distances, and likelihood ratios of the laws of Poisson point patterns in terms of their intensity measures.
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