Year: 2024
Type: article
Abstract: In this work, we show the following general property of stochastic processes: Denseness of probability distributions extends to denseness of stochastic processes. In particular, for every $$d\in \mathbb {N}$$ d ∈ N , we consider any class of probability distributions which is dense in the space of probability distributions on $$\mathbb {R}^{d}$$ R d with respect to convergence in distribution. Using these classes, we construct various explicit families of times series, continuous processes and càdlàg processes that are dense in their respective spaces with respect to convergence in distribution. This is particularly interesting because, for processes, finite-dimensional distributions convergence does not automatically imply convergence in distribution.
Author: Riccardo Passeggeri
Institution: Imperial College London
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4403816923