Active particles with fractional rotational Brownian motion

Arbitrage with Fractional Brownian Motion

Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long-range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an arbitrage. Nonetheless, it is possible by looking at a process similar to the fractional Brownian motio...

Arbitrage with Fractional Brownian Motion ?

In recent years fractional Brownian motion has been suggested to replace the classical Brownian motion as driving process in the modelling of many real world phenomena, including stock price modelling. In several papers seemingly contradictory results on the existence or absence of a riskless gain (arbitrage) in such stock models have been stated. This survey tries to clarify this issue by poin...

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

Brownian motion with active fluctuations.

We study the effect of different types of fluctuation on the motion of self-propelled particles in two spatial dimensions. We distinguish between passive and active fluctuations. Passive fluctuations (e.g., thermal fluctuations) are independent of the orientation of the particle. In contrast, active ones point parallel or perpendicular to the time dependent orientation of the particle. We deriv...