We consider the Fermi–Ulam model, which can be described as a particle moving freely between two vertical rigid walls; left one being fixed, whereas right moves according to regular periodic function. The is elastically reflected when hitting walls. show that dynamics of model by an area-preserving monotone twist map. Thus, Aubry–Mather sets exist for every rotation number in interval. Conseque...

A new method for constructing first-passage-time probability density functions in the case of regular one-dimensional time homogeneous diffusion processes restricted between constant boundaries is proposed. Some diffusion processes of particular interest in neuronal modeling are considered and thoroughly discusses.

We studied the Mean first passage time for the DNA translocation through a narrow pore. We also proved that, for an asymmetric rachet potential, the mean first passage time for the same DNA to translocate through the membrane can be different when passing from the two different ends, even without external potential. We further extended the situation to a more general case, where a periodic chai...

We develop an analytical approach that provides the dependence of the mean first-passage time (MFPT) for random walks on complex networks both on the target connectivity and on the source-target distance. Our approach puts forward two strongly different behaviors depending on the type-compact or non compact-of the random walk. In the case of non compact exploration, we show that the MFPT scales...

Interaction of capital market participants is a complicated dynamic process. A stochastic model is proposed to describe the dynamics to predict short-term stock price behaviors. Independent compound Poisson processes are introduced to describe the occurrences of market orders, limit orders, and cancellations of limit orders, respectively. Based on high-frequency observations of the limit order ...