Related papers: Stochastic search with space-dependent diffusivity
Determining whether an unknown distribution matches a known reference is a cornerstone problem in distributional analysis. While classical results establish a rigorous framework in the case of distributions over finite domains, real-world…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
Dirichlet processes and their extensions have reached a great popularity in Bayesian nonparametric statistics. They have also been introduced for spatial and spatio-temporal data, as a tool to analyze and predict surfaces. A popular…
In this paper we study macroscopic density equations in which the diffusion coefficient depends on a weighted spatial average of the density itself. We show that large differences (not present in the local density-dependence case) appear…
In this paper we consider the diffusive search for a bounded target $\Omega \in \R^d$ with its boundary $\partial \Omega$ totally absorbing. We assume that the target is surrounded by a semipermeable interface given by the closed surface…
Despite having been studied for decades, first passage processes remain an active area of research. In this contribution we examine a particle diffusing in an annulus with an inner absorbing boundary and an outer reflective boundary. We…
In performative stochastic optimization, decisions can influence the distribution of random parameters, rendering the data-generating process itself decision-dependent. In practice, decision-makers rarely have access to the true…
This paper considers the task of performing binary search under noisy decisions, focusing on the application of target area localization. In the presence of noise, the classical partitioning approach of binary search is prone to error…
Discrete diffusion models have gained increasing attention for their ability to model complex distributions with tractable sampling and inference. However, the error analysis for discrete diffusion models remains less well-understood. In…
In this review, we present the encounter-based approach to target search problems, in which the diffusive dynamics is described by the joint probability of the position of the particle and the number of its encounters with a given target…
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the…
Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter…
In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…
Spatial search problems abound in the real world, from locating hidden nuclear or chemical sources to finding skiers after an avalanche. We exemplify the formalism and solution for spatial searches involving two agents that may or may not…
Consider $(X_{i}(t))$ solving a system of $N$ stochastic differential equations interacting through a random matrix $\mathbf J = (J_{ij})$ with independent (not necessarily identically distributed) random coefficients. We show that the…
Probabilistic forecasting is crucial for real-world spatiotemporal systems, such as climate, energy, and urban environments, where quantifying uncertainty is essential for informed, risk-aware decision-making. While diffusion models have…
We extend a recently introduced prototypical stochastic model describing uniformly the search and return of objects looking for new food sources around a given home. The model describes the kinematic motion of the object with constant speed…
We determine the full distribution and moments of the first passage time for a wide class of stochastic search processes in the limit of frequent stochastic resetting. Our results apply to any system whose short-time behavior of the search…
We consider the stochastic ranking process with space-time dependent jump rates for the particles. The process is a simplified model of the time evolution of the rankings such as sales ranks at online bookstores. We prove that the joint…
The ability to uncover preferences from choices is fundamental for both positive economics and welfare analysis. Overwhelming evidence shows that choice is stochastic, which has given rise to random utility models as the dominant paradigm…