Consistent support recovery for high-dimensional diffusions

Over the past decades, statistical inference for stochastic processes has garnered increasing attention, driven by their extensive applications across diverse scientific fields. In particular, stochastic differential equations (SDEs) have proven fundamental in disciplines such as biology [38], epidemiology [6], physics [37], economics [5], neurology [25], and mathematical finance [29]. This wide applicability has spurred significant advancements in both parametric and non-parametric inference methods under various frameworks. Simultaneously, the growing importance of high-dimensional data has introduced new complexities to statistical modeling. Researchers have explored scenarios where the number of model parameters far exceeds the available observations or where most parameters exhibit specific asymptotic behavior, departing from the classical approach that assumes only the number of observations grows asymptotically. While substantial progress has been made in understanding high-dimensional frameworks for simpler models [10, 28, 42, 24], the study of high-dimensional stochastic processes remains relatively scarce. Existing work on high-dimensional diffusions has predominantly focused on particle interaction systems within mean field theory, with notable parametric and non-parametric results explored in [2, 3, 7, 8, 9, 11, 15, 23, 24, 32, 41], among others. However, most studies have restricted parameter spaces to finite dimensions, leaving the case of infinitedimensional parameter spaces underexplored. Expanding both theoretical and methodological knowledge at the intersection of high-dimensional frameworks and stochastic processes has thus become a topic of significant scientific interest.