Theory and Applications of Probability Theory and Stochastic Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 30 April 2026 | Viewed by 1120

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School of Mathematics and Statistics, Central South University, Changsha 410083, China
Interests: branching process; random walk; limit theorem progressive type; Monte Carlo; maximum likelihood estimation queueing system; Nash equilibrium; pricing

Special Issue Information

Dear Colleagues,

Probability, stochastic processes, and statistics form the mathematical backbone for understanding uncertainty, modeling dynamic random systems, and transforming data into actionable knowledge across science, engineering, and social sciences. In an era of unprecedented data complexity—characterized by high dimensionality, non-stationarity, and cross-disciplinary fusion—these fields face critical challenges, such as refining stochastic process frameworks to capture real-world temporal/spatial dependencies, advancing statistical inference under model misspecification, and integrating probabilistic methods with emerging technologies like machine learning and causal analysis.​

This Special Issue aims to showcase cutting-edge research that bridges theoretical rigor and practical impact. We welcome contributions spanning foundational advances (e.g., novel probability bounds, robust stochastic process models) and interdisciplinary applications (e.g., biostatistical modeling of disease spread, stochastic optimization in finance, probabilistic AI for decision-making). By fostering dialogue between theorists and practitioners, the Issue seeks to address modern uncertainties, from climate variability to algorithmic bias, through innovative methodological developments.

Prof. Dr. Junping Li
Guest Editor

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Keywords

  • probability theory
  • stochastic processes
  • statistical inference
  • high-dimensional data analysis
  • causal inference
  • Bayesian Methods
  • spatiotemporal modeling
  • uncertainty quantification
  • machine learning integration
  • interdisciplinary data science

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Published Papers (1 paper)

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Research

9 pages, 942 KB  
Article
A New Index for Quantifying the Peakedness of a Probability Distribution
by Hening Huang
Mathematics 2025, 13(21), 3514; https://doi.org/10.3390/math13213514 - 2 Nov 2025
Cited by 1 | Viewed by 841
Abstract
Peakedness is an important characteristic of probability distributions, and an effective method for quantifying peakedness is essential for statistical modeling and comparing different probability distributions in many practical applications. However, there has long been a misconception that kurtosis (or excess kurtosis) serves as [...] Read more.
Peakedness is an important characteristic of probability distributions, and an effective method for quantifying peakedness is essential for statistical modeling and comparing different probability distributions in many practical applications. However, there has long been a misconception that kurtosis (or excess kurtosis) serves as a measure of peakedness. In this paper, we propose a new measure for quantifying peakedness, named the “peakedness index”. For a discrete distribution, the peakedness index is defined as the ratio of the maximum (peak) probability to its discrete informity; for a continuous distribution, it is defined as the ratio of the maximum (peak) density to its continuous informity, where “informity” is a concept introduced in the recently developed theory of informity. The peakedness indices for ten well-known distributions are presented and compared with the traditional kurtosis measure. Full article
(This article belongs to the Special Issue Theory and Applications of Probability Theory and Stochastic Analysis)
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