Open Access
November 2020 Area anomaly in the rough path Brownian scaling limit of hidden Markov walks
Olga Lopusanschi, Damien Simon
Bernoulli 26(4): 3111-3138 (November 2020). DOI: 10.3150/20-BEJ1217


We study the convergence in rough path topology of a certain class of discrete processes, the hidden Markov walks, to a Brownian motion with an area anomaly. This area anomaly, which is a new object, keeps track of the time-correlation of the discrete models and brings into light the question of embeddings of discrete processes into continuous time. We also identify an underlying combinatorial structure in the hidden Markov walks, which turns out to be a generalization of the occupation time from the classical ergodic theorem in the spirit of rough paths.


Download Citation

Olga Lopusanschi. Damien Simon. "Area anomaly in the rough path Brownian scaling limit of hidden Markov walks." Bernoulli 26 (4) 3111 - 3138, November 2020.


Received: 1 September 2019; Revised: 1 March 2020; Published: November 2020
First available in Project Euclid: 27 August 2020

zbMATH: 07256170
MathSciNet: MR4140539
Digital Object Identifier: 10.3150/20-BEJ1217

Keywords: area anomaly , hidden Markov chains , Rough paths

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 4 • November 2020
Back to Top