Fibering method in some probabilistic problems

DOI10.1007/BF02116602zbMath0571.60048MaRDI QIDQ1061413

Yu. A. Davydov, Mikhail Lifshits

Publication date: 1985

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

absolute continuitydistributions of functionals of stochastic processesexistence of bounded densitiesmethod of stratification

Mathematics Subject Classification ID

General theory of stochastic processes (60G07) Sample path properties (60G17) Continuity and singularity of induced measures (60G30)

Related Items (9)

Distribution density of the norm of a stable vector ⋮ Nonuniform estimates in the central limit theorem in Banach spaces ⋮ Regularity of the laws of shot noise series and of related processes ⋮ Absolute continuity of joint laws of multiple stable stochastic integrals ⋮ On the history of the St. Petersburg school of probability and statistics. III: Distributions of functionals of processes, stochastic geometry, and extrema ⋮ Detecting deviations from second-order stationarity in locally stationary functional time series ⋮ Strong convergence of distributions of Brownian sojourn times in approximation procedures ⋮ Absolute continuity of joint laws of multiple stable integrals ⋮ Rate of convergence in the central limit theorem for empirical processes

Cites Work

• Local limit theorems for functionals of the supremum type in the lattice case
• Absolute continuity of functionals of supremum type for Gaussian processes
• Local limit theorems for functionals of random fields
• Probability distributions of the Kolmogorov and omega-square statistics for continuous distributions with shift and scale parameters
• Berry-Esseen estimates in Hilbert space and an application to the law of the iterated logarithm
• Rate of convergence in the multidimensional limit theorem with a stable limit law
• On seminorms and probabilities, and abstract Wiener spaces
• Occupation times for smooth stationary processes
• The absolute continuity of distributions of functionals of diffusion processes
• A Local Invariance Principle for Processes Linearly Generated by Independent Random Variables
• An Application of the Stratification Method to the Study of Functionals of Processes with Independent Increments
• The Expected Number of Zeros of a Stationary Gaussian Process
• Uniformity in weak convergence
• Abstract Wiener processes and their reproducing Kernel Hilbert spaces
• Rates of Convergence for Some Functionals in Probability
• Relations between Weak and Uniform Convergence of Measures with Applications
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