Bounds on the distributions of extremal values of a scanning process

DOI10.1016/0304-4149(84)90303-XzbMath0549.60066MaRDI QIDQ800046

Svante Janson

Publication date: 1984

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

upper and lower boundsPoisson processmonotonicity properties

Mathematics Subject Classification ID

Markov processes (60J99)

Related Items

Random coverings in several dimensions, Random coverings of thin sets, The analysis of the Widom-Rowlinson model by stochastic geometric methods, Corrected discrete approximations for multiple window scan statistics of one-dimensional Poisson processes, Approximations of distributions of scan statistics of inhomogeneous Poisson processes, Ellipses percolation, Localization in random geometric graphs with too many edges, The first passage sets of the 2D Gaussian free field: convergence and isomorphisms, Gibbs states over the cone of discrete measures, Multiplicative chaos of the Brownian loop soup, Stochastic Analysis for Poisson Processes, The stochastic heat equation with multiplicative Lévy noise: existence, moments, and intermittency, The Widom -- Rowlinson model under spin flip: immediate loss and sharp recovery of quasilocality, Detection and analysis of spikes in a random sequence, Spatially independent martingales, intersections, and applications, Discrete, Continuous and Conditional Multiple Window Scan Statistics, Corrected discrete approximations for the conditional and unconditional distributions of the continuous scan statistic, From loop clusters and random interlacements to the free field, Poisson approximation in connection with clustering of random points, A Compound Poisson Model for Word Occurrences in DNA Sequences

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The asymptotic distribution of the scan statistic under uniformity
• Point processes and queues. Martingale dynamics
• A simpler expression for Kth nearest neighbor coincidence probabilities
• Expected waiting time for the visual response
• On Bouman-Velden-Yamamoto's asymptotic evaluation formula for the probability of visual response in a certain experimental research in quantum-biophysics of vision
• A Poisson limit theorem for incomplete symmetric statistics
• Approximations for Distributions of Scan Statistics
• Association of Random Variables, with Applications