We prove first existence of a classical solution to class parabolic problems with unbounded coefficients on metric star graphs subject Kirchhoff-type conditions. The result is applied the Ornstein–Uhlenbeck and harmonic oscillator operators graphs. We give an explicit formula for associated semigroup unique invariant measure. show that this inherits regularity prope...

This paper aims to develop new methods for statistical inference in a class of stochastic volatility models for financial data based on non-Gaussian Ornstein-Uhlenbeck (OU) processes. Our approach uses indirect inference methods: First, a quasi-likelihood for the actual data is estimated. This quasi-likelihood is based on an approximative Gaussian state space representation of the OUbased model...

Sums of Lévy-driven Ornstein-Uhlenbeck processes seem appropriate for modelling electricity spot price data. In this paper we present a new estimation method with particular emphasis on capturing the high peaks, which is one of the stylized features of such data. After introducing our method we show it at work for the EEX Phelix Base electricity price index. We also present a small simulation s...

Motivated by second order asymptotic results, we characterize the convergence in law of double integrals, with respect to Poisson random measures, toward a standard Gaussian distribution. Our conditions are expressed in terms of contractions of the kernels. To prove our main results, we use the theory of stable convergence of generalized stochastic integrals developed by Peccati and Taqqu. One ...

In 1978 E. De Giorgi formulated a conjecture concerning the one-dimensional symmetry of bounded solutions to the elliptic equation ∆u = F ′(u), which are monotone in some direction. In this paper we prove the analogous statement for the equation ∆u−〈x,∇u〉u = F ′(u), where the Laplacian is replaced by the Ornstein-Uhlenbeck operator. Our theorem holds without any restriction on the dimension of ...