Related papers: Maximal Counts in the Stopped Occupancy Problem
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts increasing the coverage are accepted. A finite system eventually gets congested, and we study the statistics of congested…
For non-uniformly hyperbolic dynamical systems we consider the time series of maxima along typical orbits. Using ideas based upon quantitative recurrence time statistics we prove convergence of the maxima (under suitable normalization) to…
In "Recognizing the Maximum of a Sequence", Gilbert and Mosteller analyze a full information game where n measurements from an uniform distribution are drawn and a player (knowing n) must decide at each draw whether or not to choose that…
We study the revenue maximization problem with an imprecisely estimated distribution of a single buyer or several independent and identically distributed buyers given that this estimation is not far away from the true distribution. We use…
The problem of designing a profit-maximizing, Bayesian incentive compatible and individually rational mechanism with flexible consumers and costly heterogeneous supply is considered. In our setup, each consumer is associated with a…
We consider a parallel system of $m$ identical machines prone to unpredictable crashes and restarts, trying to cope with the continuous arrival of tasks to be executed. Tasks have different computational requirements (i.e., processing time…
We describe a general strategy for sampling configurations from a given (Gibbs-Boltzmann or other) distribution. It is {\it not} based on the Metropolis concept of establishing a Markov process whose stationary state is the wanted…
The drawdown process of an one-dimensional regular diffusion process $X$ is given by $X$ reflected at its running maximum. The drawup process is given by $X$ reflected at its running minimum. We calculate the probability that a drawdown…
In this paper we propose a method for the optimal allocation of observations between an intrinsically explainable glass box model and a black box model. An optimal allocation being defined as one which, for any given explainability level…
Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an…
The pinwheel problem is a real-time scheduling problem that asks, given $n$ tasks with periods $a_i \in \mathbb{N}$, whether it is possible to infinitely schedule the tasks, one per time unit, such that every task $i$ is scheduled in every…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
Stochastic games with discounted payoff, introduced by Shapley, model adversarial interactions in stochastic environments where two players try to optimize a discounted sum of rewards. In this model, long-term weights are geometrically…
Consider a storage area where arriving items are stored temporarily in bounded capacity stacks until their departure. We look into the problem of deciding where to put an arriving item with the objective of minimizing the maximum number of…
Optimization problems with stochastic dominance constraints provide a possibility to shape risk by selecting a benchmark random outcome with a desired distribution. The comparison of the relevant random outcomes to the respective benchmarks…
Crowd dynamics and many large biological systems can be described as populations of agents or particles, which can only be observed on aggregate population level. Identifying the dynamics of agents is crucial for understanding these large…
We consider zero sum stochastic games. For every discount factor $\lambda$, a time normalization allows to represent the game as being played on the interval [0, 1]. We introduce the trajectories of cumulated expected payoff and of…
We study the distribution of the maximum of a large class of Gaussian fields indexed by a box $V_N\subset Z^d$ and possessing logarithmic correlations up to local defects that are sufficiently rare. Under appropriate assumptions that…
We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…