6 papers
Schoenberg's Theorem via the law of large numbers
Davar Khoshnevisan
A classical theorem of S. Bochner states that a function is the Fourier transform of a finite Borel measure if and only if is positive definite. In 1938, I. Schoe…
An Extreme-Value Analysis of the LIL for Brownian Motion
Davar Khoshnevisan, David A. Levin, Zhan Shi
We present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian motion. Our result can be viewed as a new improvement to the LIL.
Capacities in Wiener Space, Quasi-Sure Lower Functions, and Kolmogorov's Epsilon-Entropy
Davar Khoshnevisan, David A. Levin, Pedro J. Mendez-Hernandez
We propose a set-indexed family of capacities on the classical Wiener space . This family interpolates between the Wiener measure ($\cap_{…
Images of the Brownian Sheet
Davar Khoshnevisan, Yimin Xiao
An N-parameter Brownian sheet in R^d maps a non-random compact set F in R^N_+ to the random compact set B(F) in \R^d. We prove two results on the image-set B(F): (1) It has positiv…
Exceptional Times and Invariance for Dynamical Random Walks
Davar Khoshnevisan, David A. Levin, Pedro J. Mendez-Hernandez
Consider a sequence {X(i,0) : i = 1, ..., n} of i.i.d. random variables. Associate to each X(i,0) an independent mean-one Poisson clock. Every time a clock rings replace that X-var…
Brownian Sheet and Quasi-Sure Analysis
Davar Khoshnevisan
We present a self-contained and modern survey of some existing quasi-sure results via the connection to the Brownian sheet. Among other things, we prove that quasi-every continuous…