32 citations · 46 across the 17 of their papers we have counts for
9 papers · 1 filter
The multivariate fractional Ornstein-Uhlenbeck process
Ranieri Dugo, Giacomo Giorgio, Paolo Pigato
Starting from the notion of multivariate fractional Brownian Motion introduced in [F. Lavancier, A. Philippe, and D. Surgailis. Covariance function of vector self-similar processes…
Drift estimation of the threshold Ornstein-Uhlenbeck process from continuous and discrete observations
Sara Mazzonetto, Paolo Pigato
We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at…
Density estimates and short-time asymptotics for a hypoelliptic diffusion process
Paolo Pigato
We study a system of differential equations, each in dimension . Only the first equation is forced by a Brownian motion and the dependence structure is such that, under a lo…
Maximum likelihood drift estimation for a threshold diffusion
Antoine Lejay, Paolo Pigato
We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and neg…
Statistical estimation of the Oscillating Brownian Motion
Antoine Lejay, Paolo Pigato
We study the asymptotic behavior of estimators of a two-valued, discontinuous diffusion coefficient in a Stochastic Differential Equation, called an Oscillating Brownian Motion. Us…
Diffusions under a local strong Hörmander condition. Part II: tube estimates
Vlad Bally, Lucia Caramellino, Paolo Pigato
We study lower and upper bounds for the probability that a diffusion process in remains in a tube around a skeleton path up to a fixed time. We assume that the diffu…
Diffusions under a local strong Hörmander condition. Part I: density estimates
Vlad Bally, Lucia Caramellino, Paolo Pigato
We study lower and upper bounds for the density of a diffusion process in in a small (but not asymptotic) time, say . We assume that the diffusion coefficients…
Tube estimates for diffusion processes under a weak Hörmander condition
Paolo Pigato
We consider a diffusion process under a local weak Hörmander condition on the coefficients. We find Gaussian estimates for the density in short time and exponential lower and upper…
Multi-scaling of moments in stochastic volatility models
Paolo Dai Pra, Paolo Pigato
We introduce a class of stochastic volatility models for which the absolute moments of the increments exhibit anomalous scaling: $\E\left(|X_{t+h} - X_t|^q \righ…