Concept

Almost surely

Related publications (11)

Preconditioners for robust optimal control problems under uncertainty

The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random realizations. Despite its ...

2022

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Volkan Cevher, Ali Kavis, Shaul Nadav Hallak

This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm’s convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and converges with prob ...

2020

The probability of intransitivity in dice and close elections

Jan Hazla

We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for n-sided dice with pairwise ordering induced by the probability, relative to 1/2, that a throw from one die is higher than the other. We ...

2020

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

Fei Pu

In this thesis, we study systems of linear and/or non-linear stochastic heat equations and fractional heat equations in spatial dimension

1

driven by space-time white noise. The main topic is the study of hitting probabilities for the solutions to these ...

EPFL2018

Semiparametric Bayesian Risk Estimation for Complex Extremes

Thomas Lugrin

Extreme events are responsible for huge material damage and are costly in terms of their human and economic impacts. They strike all facets of modern society, such as physical infrastructure and insurance companies through environmental hazards, banking an ...

EPFL2018

Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures

Emeric Rolland Georges Thibaud, Raphaël Huser

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect depen ...

Elsevier Sci Ltd2017

The Range of a Random Walk on a Comb

János Pach, Gábor Tardos

The graph obtained from the integer grid Z x Z by the removal of all horizontal edges that do not belong to the x-axis is called a comb. In a random walk on a graph, whenever a walker is at a vertex v, in the next step it will visit one of the neighbors of ...

Electronic Journal Of Combinatorics2013

Multitype Contact Process on Z: Extinction and Interface

Daniel Rodrigues Valesin

We consider a two-type contact process on Z in which both types have equal finite range and supercritical infection rate. We show that a given type becomes extinct with probability 1 if and only if, in the initial configuration, it is confined to a finite ...

2010

Criteria for hitting probabilities with applications to systems of stochastic wave equations

Robert Dalang

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these ...

2010

Probabilistic Weighted Automata

Laurent Doyen

Nondeterministic weighted automata are finite automata with numerical weights on transitions. They define quantitative languages

L

that assign to each word

w

a real number

L(w)

. The value of an infinite word

w

is computed as the maximal value of al ...

2009

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.