The book is devoted to the fundamental relationship between three objects: a stochastic
process, stochastic differential equations driven by that process and their associated Fokker …

Fractional calculus has emerged as a powerful and effective mathematical tool in the study
of several phenomena in science and engineering. This text addressed to researchers …

There is by now an extensive and well-developed theory of weak convergence for moving
averages and continuous-time random walks (CTRWs) with respect to Skorokhod's M1 and …

Abstract The Ornstein–Uhlenbeck process is one of the most popular systems used for
financial data description. However, this process has also been examined in the context of …

The rate of strong convergence is investigated for an approximation scheme for a class of
stochastic differential equations driven by a time-changed Brownian motion, where the …

Abstract Continuous Time Random Walk models (CTRW) of anomalous diffusion are
studied, where the anomalous exponent β (x)∈(0, 1) varies in space. This type of situation …

The stability of nonlinear stochastic differential equations driven by time-changed Lévy
process with impulsive effects is discussed in this paper. Some sufficient conditions are …

The Lévy Walk is the process with continuous sample paths which arises from consecutive
linear motions of iid lengths with iid directions. Assuming speed 1 and motions in the domain …

We define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional
Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of …

There is a well-known relationship between the Itô stochastic differential equations (SDEs)
and the associated partial differential equations called Fokker-Planck equations, also called …