8 citations · 9 across the 12 of their papers we have counts for
14 papers
Algorithms for Robbins' Problem using Markov Decision Processes
Léonard Brice, F. Thomas Bruss, Anirban Majumdar +1
In this paper, we consider Robbins' problem, which is a full information variant of the well-known secretary selection problem. In this version of the problem, the goal is to minim…
Win rates at first-passage times for biased simple random walks
F. Thomas Bruss, Davy Paindaveine
We study the win rate of a biased simple random walk on at the first-passage time , with . Using g…
Gambling under unknown probabilities as a proxy for real world decisions under uncertainty
David J. Aldous, F. Thomas Bruss
We give elementary examples within a framework for studying decisions under uncertainty where probabilities are only roughly known. The framework, in gambling terms, is that the si…
Mathematical intuition, deep learning, and Robbins' problem
F. Thomas Bruss
{\bf Abstract.} The present article is an essay about mathematical intuition and Artificial intelligence (A.I.), followed by a guided excursion to a well-known open problem. It has…
Galton-Watson processes and their role as building blocks for branching processes
F. Thomas Bruss
This article is an essay, both expository and argumentative, on the Galton-Watson process as a tool in the domain of Branching Processes. It is at the same time the author's ways t…
Answer to an open question concerning the -strategy for best choice under no information
F. Thomas Bruss, L. C. G. Rogers
This paper answers a long-standing open question concerning the -strategy for the problem of best choice. candidates for a job arrive at times independently uniformly dist…
The BRS-inequality and its Applications A Survey
F. Thomas Bruss
This article is a survey of results concerning an inequality, which may be seen as a versatile tool to solve problems in the domain of Applied Probability. The inequality, which we…
On the -strategy for the best-choice problem under no information
F. Thomas Bruss
The main purpose of this paper is to correct an error in the previously submitted version [*] := arXiv:2004.13749v1. [*] had been already accepted for publication in a scientific j…
Numerical Aspects of Computing Possible Equilibria for Resource Dependent Branching Processes with Immigration
F. Thomas Bruss
This article studies the stability of solutions of equilibrium equations arising in so-called resource dependent branching processes. We argue that these new models, building on th…
Odds-Theorem and Monotonicity
F. Thomas Bruss
Given a finite sequence of events and a well-defined notion of events being interesting, the Odds-theorem (Bruss (2000)) gives an online strategy to stop on the last interesting ev…
Equilibrium Equations for Human Populations with Immigration
F. Thomas Bruss
The objective of this article is to create a framework to study asymptotic equilibria in human populations with a special focus on immigration. We present a new model, based on Res…
A Mathematical Approach to Comply with Ethical Constraints in Compassionate Use Treatments
F. Thomas Bruss
Patients who are seriously ill may ask doctors to treat them with unapproved medication, about which not much is known, or else with known medication in a high dosage. Apart from s…
Last-Hitting Times and Williams' Decomposition of the Bessel Process of Dimension 3 at its Ultimate Minimum
F. Thomas Bruss, Marc Yor
In this note we shortly recall the importance of last-hitting times in theory and applications of optimal stopping. As a small contribution to this domain we then propose a concise…
Resource dependent branching processes and the envelope of societies
F. Thomas Bruss, Mitia Duerinckx
Since its early beginnings, mankind has put to test many different society forms, and this fact raises a complex of interesting questions. The objective of this paper is to present…