The hole probability that the zero set of the time dependent planar Gaussian analytic function fC(z, t) = ∞ ∑ n=0 an(t) zn √ n! , (1) where an(t) are i.i.d. complex valued Ornstein-Uhlenbeck processes, does not intersect a disk of radius R for all t ∈ [0, T ] decays like exp(−TecR2). This result sharply differentiates the zero set of fC from a number of canonical evolving planar point processes...

We consider the Kuramoto model of globally coupled phase oscillators subject to Ornstein-Uhlenbeck and non-Gaussian colored noise and investigate the influence of noise on the order parameter of the synchronization process. We use numerical methods to study the dependence of the threshold as well as the maximum degree of synchronization on the correlation time and the strength of the noise, and...

Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order structure of the volatility, the log returns, as well as their “squares” are discussed in detail. M...

Jaume Masoliver‡ Departament de F́ısica Fonamental, Universitat de Barcelona, Diagonal, 647, E-08028 Barcelona, Spain (Dated: May 28, 2008) Abstract We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a ...