3 papers
math.PR2018
Ballistic random walks in random environment as rough paths: convergence and area anomaly
Olga Lopusanschi, Tal Orenshtein
Annealed functional CLT in the rough path topology is proved for the standard class of ballistic random walks in random environment. Moreover, the `area anomaly', i.e. a determinis…
math.PR2017
Area anomaly in the rough path Brownian scaling limit of hidden Markov walks
Olga Lopusanschi, Damien Simon
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, whi…
math.PR2016
Lévy area with a drift as a renormalization limit of Markov chains on periodic graphs
Olga Lopusanschi, Damien Simon
A careful look at rough path topology applied to Brownian motion reveals new possible properties of the well-known Lévy area, in particular the presence of an intrinsic drift of th…