The section we propose will be dedicated to exploring the realm of stochastic processes as a tool for addressing complex challenges across various disciplines. In this session, we aim to delve into the applications of stochastic processes, with a particular emphasis on ecology, natural sciences, neuroscience, and physics. Through insightful discussions and presentations, we seek to highlight the role of statistical methods in elucidating intricate phenomena and driving innovative solutions.

The session will feature presentations from five distinguished speakers, each a specialist in the field of statistics for stochastic processes. Through their expertise and research contributions, our speakers will showcase the versatility and efficacy of stochastic processes in tackling real-world problems. From ecological modelling to neuronal data analysis, our session will encompass a diverse array of applications, underscoring the broad impact of statistical methodologies.

The key themes are: 

Ecological modelling, climatology and environmental sciences: these topics will be developed by Susanne Ditlevsen, full professor at the University of Copenhagen, who will talk about how to estimate tipping points in climate and ecosystems, and Charlotte Dion, assistant professor at Sorbonne University, who will discuss how to use Hawkes processes as a tool for classifying foraging and commuting behaviour of bats at a site.

Applications in neuroscience and in biomolecular models: these topics will be developed by Céline Duval, full professor at the University of Lille, and by Daniele Cappelletti, postdoctoral researcher at the Polytechnic University of Turin. Céline Duval will present results for a general class of mean-field interacting nonlinear Hawkes processes modelling the reciprocal interactions between two neuronal populations, while Daniele Cappelletti will focus on Markovian models of chemical networks that can gain or lose positive recurrence if rates are stochastic processes.

Nonparametric statistics for SPDE’s: this topic will be developed by Randolf Altmeyer, assistant professor in the Department of Pure Mathematics and Mathematical Statistics in Cambridge, who will focus on the problem of nonparametric estimation in a second order linear stochastic partial differential equation with additive noise.