We consider a stochastic differential equation involving a pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according to first- and second-order quadratic variations of observed values of the solution. The rate of convergence of...

In this paper we introduce a new perspective of linear prediction in the functional data context that predicts a scalar response by observing a functional predictor. This perspective broadens the scope of functional linear prediction currently in the literature, which is exclusively focused on...

The Axelrod model is a spatial stochastic model for the dynamics of cultures which, similar to the voter model, includes social influence, but differs from the latter by also accounting for another social factor called homophily, the tendency to interact more frequently with individuals who are...

The purpose of this paper is to show how one can extend some results on disorder relevance obtained for the random pinning model with i.i.d disorder to the model with finite range correlated disorder. In a previous work, the annealed critical curve of the latter model was computed, and equality...

For the Ornstein–Uhlenbeck process, the asymptotic behavior of the maximum likelihood estimator of the drift parameter is totally different in the stable, unstable, and explosive cases. Notwithstanding this trichotomy, we investigate sharp large deviation principles for this estimator in the...

Some fractional and anomalous diffusions are driven by equations involving fractional derivatives in both time and space. Such diffusions are processes with randomly varying times. In representing the solutions to those equations, the explicit laws of certain stable processes turn out to be...

We give an extension of Hoeffding’s inequality to the case of supermartingales with differences bounded from above. Our inequality strengthens or extends the inequalities of Freedman, Bernstein, Prohorov, Bennett and Nagaev.

We consider the effect of recovery rates on a pool of credit assets. We allow the recovery rate to depend on the defaults in a general way. Using the theory of large deviations, we study the structure of losses in a pool consisting of a continuum of types. We derive the corresponding rate...

We consider the problem of adaptive estimation of the regression function in a framework where we replace ergodicity assumptions (such as independence or mixing) by another structural assumption on the model. Namely, we propose adaptive upper bounds for kernel estimators with data-driven...

We construct a confined Langevin type process aimed to satisfy a mean no-permeability condition at the boundary. This Langevin process lies in the class of conditional McKean Lagrangian stochastic models studied by Bossy, Jabir and Talay (2010) [5]. The confined process considered here is a...