A new class of stochastic processes, termed Brownian semistationary processes (BSS), is
introduced and discussed. This class has similarities to that of Brownian semimartingales …

The question of existence and properties of stationary solutions to Langevin equations
driven by noise processes with stationary increments is discussed, with particular focus on …

Stationary infinitely divisible processes Page 1 Brazilian Journal of Probability and Statistics
2011, Vol. 25, No. 3, 294–322 DOI: 10.1214/11-BJPS140 © Brazilian Statistical Association …

This paper develops a stochastic integration theory with respect to volatility modulated Lévy-
driven Volterra (V MLV) processes. It extends recent results in the literature to allow for …

By employing the technique of enlargement of filtrations, we demonstrate how to incorporate
information about the future trend of the stochastic interest rate process into a financial …

Stricker's theorem states that a Gaussian process is a semimartingale in its natural filtration if
and only if it is the sum of an independent increment Gaussian process and a Gaussian …

We study the asymptotics of lattice power variations of two-parameter ambit fields driven by
white noise. Our first result is a law of large numbers for power variations. Under a constraint …

In the present paper we study moving averages (also known as stochastic convolutions)
driven by a Wiener process and with a deterministic kernel. Necessary and sufficient …

The aim of the present paper is to characterize the spectral representation of Gaussian
semimartingales. That is, we provide necessary and sufficient conditions on the kernel K for …

We define a two-parameter family of Gaussian Markov processes, which includes Brownian
motion as a special case. Our main result is that any centered self-similar Gaussian Markov …