Many phylogenetic comparative methods that are currently widely used in the scientific literature assume a Brownian motion model for trait evolution, but the suitability of that model is rarely tested, and a number of important factors might affect whether this model is appropriate or not. For instance, we might expect evolutionary change in adaptive radiations to be driven by the availability ...

Abstract. The importance of identification and adaptive control of continuous-time stochastic systems are discussed. Recent developments of stochastic calculus of fractional Brownian motion and its appications to stochastic differential equations are presented. Applications of presented stochastic theory to epilepsy are shown. The educational aspects of stochastic analysis and control are discu...

We propose a path transformation which applied to a cyclically exchangeable increment process conditions its minimum to belong to a given interval. This path transformation is then applied to processes with start and end at 0. It is seen that, under simple conditions, the weak limit as ε → 0 of the process conditioned on remaining above −ε exists and has the law of the Vervaat transformation of...

Asymptotically one-dimensional diffusions on the Sierpinski gasket constitute a one parameter family of processes with significantly different behaviour to the Brownian motion. Due to homogenization effects they behave globally like the Brownian motion, yet locally they have a preferred direction of motion. We calculate the spectral dimension for these processes and obtain short time heat kerne...