Fractional Brownian Motion and the Markov Property

The Strong Markov Property of the Brownian Motion

LAN property for some fractional type Brownian motion

We study asymptotic expansion of the likelihood of a certain class of Gaussian processes characterized by their spectral density fθ. We consider the case where fθ(x) ∼x→0 |x|Lθ(x) with Lθ a slowly varying function and α(θ) ∈ (−∞, 1). We prove LAN property for these models which include in particular fractional Brownian motion or ARFIMA processes.

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Lacunary Fractional Brownian Motion

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Tempered fractional Brownian motion