Stochastic volatility modelling of financial processes has become increasingly popular. The proposed models usually contain a stationary volatility process. We will motivate and review several nonparametric methods for estimation of the density of the volatility process. Both models based on...

In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional diffusion. The drift is modeled by a scaled linear...

In this paper we consider the use of Brownian motion as a prior in a nonparametric, univariate regression setting. Using change of measure theory for continuous semimartingales we derive an explicit stochastic differential equation characterization for the posterior. In combination with...

We study and answer the question posed in the title. The answer is derived from some new necessary and sufficient conditions for equivalence of Gaussian processes with stationary increments and recent frequency domain results for the fBm. The result shows in particular precisely in which cases...

We show that an explicit series expansion of the fractional Brownian motion derived by Dzhaparidze and Van Zanten (Probab. Theory Related Fields 130 (1) (2004) 39) is rate-optimal in the sense that the expected uniform norm of the truncated series vanishes at the optimal rate as the truncation...

In this paper, we show that the moving average and series representations of fractional Brownian motion can be obtained using the spectral theory of vibrating strings. The representations are shown to be consequences of general theorems valid for a large class of second-order processes with...