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Multivariate normal approximation using exchangeable pairs
Stein's method exchangeable pairs normal approximation random matrices
2009/6/12
The aim of this article is to fill this void.We present three abstract normal approximation theorems using exchangeable pairs in multivariate contexts,one for situations in which the underlying symmet...
The lower tail problem for homogeneous functionals of stable processes with no negative jumps
lower tail problem homogeneous functionals stable processes negative jumps
2009/6/12
The lower tail problem for homogeneous functionals of stable processes with no negative jumps.
Some random times and martingales associated with BES0(δ) processes (0<δ<2)
random times martingales BES0(δ) processes
2009/6/12
Some random times and martingales associated with BES0(δ) processes (0<δ<2).
Spatial birth and death processes as solutions of stochastic equations
spatial birth death processes stochastic equations
2009/6/12
Spatial birth and death processes as solutions of stochastic equations .
Exponential functionals of Brownian motion, I: Probability laws at fixed time
Brownian motion Bessel process Lamperti's relation Hartman-Watson distributions
2009/5/18
This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several rel...
This survey paper is based on mini-courses given in July 2003 at the University of St-Andrews, and at the ICMS in Edinburgh. Its goal is to give a self-contained overview of the recent (i.e. pre-2003)...
Stochastic differential equations with jumps
stochastic differential equations jumps martingale problems pathwise uniqueness Harnack inequality
2009/5/18
This paper is a survey of uniqueness results for stochastic differential equations with jumps and regularity results for the corresponding harmonic functions.
Level crossings and other level functionals of stationary Gaussian processes
Gaussian processes/fields Hermite polynomials level curve level functionals local time (factorial) moments
2009/5/18
This paper presents a synthesis on the mathematical work done on level crossings of stationary Gaussian processes, with some extensions. The main results [(factorial) moments, representation into the ...
Brownian excursion area, Wright's constants in graph enumeration, and other Brownian areas
Brownian excursion area graph enumeration
2009/5/18
This survey is a collection of various results and formulas by different authors on the areas (integrals) of five related processes, viz. Brownian motion, bridge, excursion, meander and double meander...
The notion of ψ-weak dependence and its applications to bootstrapping time series
Autoregressive processes autoregressive bootstrap mixing weak dependence.
2009/5/18
We give an introduction to a notion of weak dependence which is more general than mixing and allows to treat for example processes driven by discrete innovations as they appear with time series bootst...
Transportation Approach to Some Concentration Inequalities in Product Spaces
Concentration Inequalities Product Spaces Transportation
2009/5/12
Let P be any product (Borel) probability measure on product (Polish) space E and for vectors x,y,z in E let f(x,y,z) be the number of coordinates k for which x_k neither equals y_k nor z_k. Using a tr...
Martingale Representation and a Simple Proof of Logarithmic Sobolev Inequalities on Path Spaces
Martingale Representation Logarithmic Sobolev Inequality Hypercontractivity PathSpace
2009/5/8
We show how the Clark-Ocone-Haussmann formula for Brownian motion on a compact Riemannian manifold put forward by S. Fang in his proof of the spectral gap inequality for the Ornstein-Uhlenbeck operato...
The Distribution of Time Spent by a Standard Excursion Above a Given Level, with Applications to Ring Polymers near a Discontinuity in Potential
Standard Brownian Excursions Brownian Bridges Ring Polymers End-Attached Polymers
2009/5/8
The law for the time tau_{a} spent by a standard Brownian excursion above a given level a>0 is found using Ito excursion theory. This is achieved by conditioning the excursion to have exactly one mark...
Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collec...
We sharpen a bound in a theorem of Russell Lyons for percolation on a tree and associated random walk.