In the present paper we study asymptotic behavior of auto-covariance function for Ornstein–Uhlenbeck (OU) processes driven by Gaussian noises with stationary and non-stationary increments Hermite OU processes. Our results are generalizations corresponding Cheridito et al. Kaarakka Salminen.

‎in this paper lie symmetry analysis is applied in order to find new solutions for fokker plank equation of ornstein-uhlenbeck process‎. ‎this analysis classifies the solutions format of the fokker plank equation by using the lie algebra of the symmetries of our considered stochastic process‎.

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...

We investigate the asymptotic properties of the minimum L1-norm estimator of the drift parameter for fractional Ornstein-Uhlenbeck type process satisfying a linear stochastic differential equation driven by a fractional Brownian motion.