Regression models and their statistical analyses is the most important tool used by scientists in data analyses especially for modeling the relationship among random variables and making predictions with higher accuracy. A fundamental problem in the theory of errors, which has drawn attention of leading mathematicians and scientists since past few centuries, was that of fitting functions. For t...

We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the √ t-behavior of reaction penetration depths by including non-linear effects due to deviations from the classical Henry’s law and time-dependent Dirichlet data.

We study right tail large deviations of the logarithm of the partition function for directed lattice paths in i.i.d. random potentials. The main purpose is the derivation of explicit formulas for the 1+1-dimensional exactly solvable case with log-gamma distributed random weights. Along the way we establish some regularity results for this rate function for general distributions in arbitrary dim...

In the title compound, 2C(4)H(6)N(3) (+)·SO(4) (2-), the cations are each essentially planar with r.m.s. deviations of the fitted atoms of 0.008 and 0.002 Å. In the crystal, adjacent ions are linked by N-H⋯O, C-H⋯O and C-H⋯N hydrogen bonds, forming a three-dimensional network.

We study large deviations for the renormalized self-intersection local time of d-dimensional stable processes of index β ∈ (2d/3, d]. We find a difference between the upper and lower tail. In addition, we find that the behavior of the lower tail depends critically on whether β < d or β = d.

We consider a problem that combines impulse control with absolutely continuous control of the drift of a general one-dimensional Itô diffusion. The objective of the control problem is to minimise an ergodic or long-term average criterion that penalises both deviations of the state process from a given nominal point and the use of control effort. Our analysis completely characterises the optimal...

Abstract. A Boussinesq model for the Bénard convection under random influences is considered as a system of stochastic partial differential equations. This is a coupled system of stochastic Navier-Stokes equations and the transport equation for temperature. Large deviations are proved, using a weak convergence approach based on a variational representation of functionals of infinite dimensional...

In this paper we derive estimates of the sample sizes required to solve a multistage stochastic programming problem with a given accuracy by the (conditional sampling) sample average approximation method. The presented analysis is self contained and is based on a, relatively elementary, one dimensional Cramér’s Large Deviations Theorem.

This paper is based on Wald Lectures given at the annual meeting of the IMS in Minneapolis during August 2005. It is a survey of the theory of large deviations. 1. Large deviations for sums. The role of " large deviations " is best understood through an example. Suppose that X random variables, for instance, normally distributed with mean zero and variance 1. Then, E e θ(X 1 +···+X n) = E[e θX ...

1 Mining public transportation networks is a growing and explosive challenge due to the increasing number of information available. In highly populated urban zones, the vehicles can often fail the schedule. Such fails cause headway deviations (HD) between high-frequency bus pairs. In this paper, we propose to identify systematic HD which usually provokes the phenomenon known as Bus Bunching (BB...