In this paper, the probability density functions (PDFs) of scalar stochastic differential
equations (SDEs) subject to α-stable Lévy white noise are investigated. The path integral …

Stochastic perturbations and periodic excitations are generally regarded as sources to
induce critical transitions in complex systems. However, we find that they are also able to …

The probability density function of the stochastic differential equations with α α-stable Lévy
noise is determined by the deterministic fractional Fokker–Planck (FFP) equation with the …

Heterogeneous diffusion processes (HDPs) with space-dependent diffusion coefficients D
(x) are found in a number of real-world systems, such as for diffusion of macromolecules or …

The filtering issue of a nonlinear system with colored non-stationary heavy-tailed
measurement noise (CNSHMN) is addressed in this study via designing a new Gaussian …

The enhanced transport of particles by roughness in a tilted rough ratchet potential subject
to a Lévy noise is investigated in this paper. Due to the roughness, the transport process …

In this paper, we investigate the first-passage-time distribution (FPTD) within a time-
dependent parabolic potential in the presence of roughness with two methods: the Kramers …

Absolute negative mobility, where particles move opposite to the direction as governed by
the external load, is an anomalous transport property of a Brownian ratchet and has …

Synchronization plays an important role in propelling microrobots, especially for those
driven by an external magnetic field. Here, we substantially contribute to the understanding …

The escape from a potential well is an archetypal problem in the study of stochastic
dynamical systems, representing real-world situations from chemical reactions to leaving an …