Alessandro De Gregorio

Least Squares Volatility Change Point Estimation for Partially Observed Diffusion Processes

A one-dimensional diffusion process X = {X t , 0 ≤ t ≤ T}, with drift b(x) and diffusion coefficient known up to θ > 0, is supposed to switch volatility regime at some point t* ∈ (0,T). On the basis of discrete time observations from X, the problem is the one of estimating the instant of change in the volatility structure t* as well as the two values of θ, say θ1 and θ2, before and after the change point. It is assumed that the sampling occurs at regularly spaced times intervals of length Δ n with nΔ n = T. To work out our statistical problem we use a least squares approach. Consistency, rates of convergence and distributional results of the estimators are presented under an high frequency scheme. We also study the case of a diffusion process with unknown drift and unknown volatility but constant.

On Rényi information for ergodic diffusion processes

In this paper, we derive explicit formulas of the Renyi information, Shannon entropy and Song measure for the invariant density of one dimensional ergodic diffusion processes. In particular, the diffusion models considered include the hyperbolic, the generalized inverse Gaussian, the Pearson, the exponential family and a new class of skew-t diffusions.

A family of random walks with generalized Dirichlet steps

We analyze a class of continuous time random walks in

On Random Flights with Non-uniformly Distributed Directions

\mathbb R^d,d\geq 2,

Adaptive lasso-type estimation for multivariate diffusion processes

with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes of orientation, we provide the analytic form of the probability density function of the position

Least-squares change-point estimation for the telegraph process observed at discrete times

\{\underline{\bf X}_d(t),t>0\}

Stochastic velocity motions and processes with random time

reached, at time

On the Asymptotic Behavior of the Hyperbolic Brownian Motion

t>0

Large Deviations for a Damped Telegraph Process

, by the random motion. In particular, we analyze the case of random walks with two steps. In general, it is an hard task to obtain the explicit probability distributions for the process

On penalized estimation for dynamical systems with small noise

\{\underline{\bf X}_d(t),t>0\}