Related papers: Random walkers with extreme value memory: modellin…
Recommendations based on behavioral data may be faced with ambiguous statistical evidence. We consider the case of association rules, relevant e.g.~for query and product recommendations. For example: Suppose that a customer belongs to…
As a firm varies the price of a product, consumers exhibit reference effects, making purchase decisions based not only on the prevailing price but also the product's price history. We consider the problem of learning such behavioral…
We review the question of the extreme values attained by a random process. We relate it to level crossings either to one boundary (first-passage problems) and two boundaries (escape problems). The extremes studied are the maximum, the…
We study the phenomenon of weak ergodicity breaking for a class of globally correlated random walk dynamics defined over a finite set of states. The persistence in a given state or the transition to another one depends on the whole previous…
We identify a fundamental phenomenon of heterogeneous one dimensional random walks: the escape (traversal) time is maximized when the heterogeneity in transition probabilities forms a pyramid-like potential barrier. This barrier corresponds…
When making decisions under risk, people often exhibit behaviors that classical economic theories cannot explain. Newer models that attempt to account for these irrational behaviors often lack neuroscience bases and require the introduction…
We investigate the distribution and multiple occurrences of extreme events stochastic processes constructed by sampling the solution of a Stochastic Differential Equation on $\mathbb{R}^n$. We do so by studying the action of an annealead…
We study the problem of learning to bid when the bidder's value is dynamic, i.e., when the current value depends on past outcomes. Specifically, we consider a bidder participating in repeated second-price auctions whose value depends on the…
We study, in d-dimensions, the random walker with geometrically shrinking step sizes at each hop. We emphasize the integrated quantities such as expectation values, cumulants and moments rather than a direct study of the probability…
We investigate extreme value theory of a class of random sequences defined by the all-time suprema of aggregated self-similar Gaussian processes with trend. This study is motivated by its potential applications in various areas and its…
We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16},…
We consider the random connection model in which an edge between two Poisson points at distance $r$ is present with probability $g(r)$. We conduct an extreme value analysis on this model, namely by investigating the longest edge with at…
Reinforcement learning systems are often concerned with balancing exploration of untested actions against exploitation of actions that are known to be good. The benefit of exploration can be estimated using the classical notion of Value of…
Large language model-powered multi-agent systems have emerged as powerful tools for simulating complex human-like systems. The interactions within these systems often lead to extreme events whose origins remain obscured by the black box of…
We consider a model where an agent has a repeated decision to make and wishes to maximize their total payoff. Payoffs are influenced by an action taken by the agent, but also an unknown state of the world that evolves over time. Before…
We present a random walk model that exhibits asymptotic subdiffusive, diffusive, and superdiffusive behavior in different parameter regimes. This appears to be the first instance of a single random walk model leading to all three forms of…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…
In this paper we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree…
Flood quantile estimation is of great importance for many engineering studies and policy decisions. However, practitioners must often deal with small data available. Thus, the information must be used optimally. In the last decades, to…
Tasks that require information about the world imply a trade-off between the time spent on observation and the variance of the response. In particular, fast decisions need to rely on uncertain information. However, standard estimates of…