Stochastic Analysis of Gaussian Processes via Fredholm Representation

We show that every separable Gaussian process with integrable variance function admits a Fredholm representation with respect to a Brownian motion. We extend the Fredholm representation to a transfer principle and develop stochastic analysis by using it. We show the convenience of the Fredholm representation by giving applications to equivalence in law, bridges, series expansions, stochastic differential equations and maximum likelihood estimations

Parameter Estimation for the Langevin Equation with Stationary-Increment Gaussian Noise

We study the Langevin equation with stationary-increment Gaussian noise. We show the strong consistency and the asymptotic normality with Berry--Esseen bound of the so-called alternative estimator of the mean reversion parameter. The conditions and results are stated in terms of the variance function of the noise. We consider both the case of continuous and discrete observations. As examples we consider fractional and bifractional Ornstein--Uhlenbeck processes. Finally, we discuss the maximum likelihood and the least squares estimators

Integral representation with adapted continuous integrand with respect to fractional Brownian motion

We show that if a random variable is a final value of an adapted Holder continuous process, then it can be represented as a stochastic integral with respect to fractional Brownian motion, and the integrand is an adapted process, continuous up to the final point

Conditional-Mean Hedging Under Transaction Costs in Gaussian Models

We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an application, we consider conditional-mean hedging under transaction costs in Black-Scholes type pricing models where the Brownian motion is replaced with a more general regular invertible Gaussian Volterra process.Comment: arXiv admin note: text overlap with arXiv:1706.0153

Prediction Law of fractional Brownian Motion

We calculate the regular conditional future law of the fractional Brownian motion with index $H\in(0,1)$ conditioned on its past. We show that the conditional law is continuous with respect to the conditioning path. We investigate the path properties of the conditional process and the asymptotic behavior of the conditional covariance