EuDML | Browse

Page 1

Displaying 1 – 5 of 5

Ergodic control of linear stochastic equations in a Hilbert space with fractional Brownian motion

Tyrone E. Duncan, B. Maslowski, B. Pasik-Duncan (2015)

Banach Center Publications

A linear-quadratic control problem with an infinite time horizon for some infinite dimensional controlled stochastic differential equations driven by a fractional Brownian motion is formulated and solved. The feedback form of the optimal control and the optimal cost are given explicitly. The optimal control is the sum of the well known linear feedback control for the associated infinite dimensional deterministic linear-quadratic control problem and a suitable prediction of the adjoint optimal system...

Ergodicity of increments of the Rosenblatt process and some consequences

Petr Čoupek, Pavel Křížek, Bohdan Maslowski (2025)

Czechoslovak Mathematical Journal

A new proof of the mixing property of the increments of Rosenblatt processes is given. The proof relies on infinite divisibility of the Rosenblatt law that allows to prove only the pointwise convergence of characteristic functions. Subsequently, the result is used to prove weak consistency of an estimator for the self-similarity parameter of a Rosenblatt process, and to prove the existence of a random attractor for a random dynamical system induced by a stochastic reaction-diffusion equation driven...

Erratum to “Number variance from a probabilistic perspective, infinite systems of independent Brownian motions and symmetric $α$ -stable processes".

Hambly, Ben M., Jones, Lisa M. (2009)

Electronic Journal of Probability [electronic only]

Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion.

Breton, Jean-Christophe, Nourdin, Ivan (2008)

Electronic Communications in Probability [electronic only]

Extrapolation in fractional autoregressive models

Jiří Anděl, Georg Neuhaus (1998)

Kybernetika

The naïve and the least-squares extrapolation are investigated in the fractional autoregressive models of the first order. Some explicit formulas are derived for the one and two steps ahead extrapolation.