Since the 60s of last century Fractional Calculus exhibited a remarkable progress and
presently it is recognized to be an important topic in the scientific arena. This survey …

Full article: Martingales for physicists: a treatise on stochastic thermodynamics and beyond
Skip to Main Content Taylor and Francis Online homepage Browse Search Publish Login …

Modern microscopic techniques following the stochastic motion of labelled tracer particles
have uncovered significant deviations from the laws of Brownian motion in a variety of …

Long-memory, or more generally fractal, processes are known to play an important role in
many scientific disciplines and applied fields such as physics, geophysics, hydrology …

5 Stochastic Differential Equations Page 1 5 Stochastic Differential Equations 5.1 Examples
and Some Solution Methods We now return to the possible solutions Xt(ω) of the stochastic …

Fix a domain\mathcal S ⊂ R^ k (our solvency region) and let Y (t)= Y^(u)(t) be a stochastic
process of the form d Y (t) &= b (Y (t), u (t)) d t+ σ (Y (t), u (t)) d B (t)\nonumber\&\quad+ ∫ …

This volume examines the theory of fractional Brownian motion and other long-memory
processes. Interesting topics for PhD students and specialists in probability theory …

In this chapter we will apply the general theory developed in Chapter 2 to solve various
stochastic partial differential equations (SPDEs). In fact, as pointed out in Chapter 1, our …

Fractional processes are widely found in science, technology and engineering systems. In
Fractional Processes and Fractional-order Signal Processing, some complex random …

As is well-known, the classical Brownian motion is a stochastic process which is selfsimilar
of index 1/2 and has stationary increments. It is actually the only continuous Gaussian …