Itô’s stochastic calculus: Its surprising power for applications

Stochastic Calculus and Applications

These notes and other information about the course are available on www.statslab.cam.ac.uk/∼beresty/teach/StoCal/stocal.html Christina Goldschmidt, Stefan Grosskinsky, Gregory Miermont, and James Norris have all contributed to these notes. However, errors are my responsibility only. Comments and corrections are most welcome and should be sent to N.Berestycki AT statslab.cam.ac.uk Date last modi...

Quantum Stochastic Calculus and Some Of Its Applications

We describe the main features of the Hudson-Parthasarathy quantum stochastic calculus and some of its applications to systems control and, recently, to quantum economics.

Fractional calculus and its applications.

Fractional calculus was formulated in 1695, shortly after the development of classical calculus. The earliest systematic studies were attributed to Liouville, Riemann, Leibniz, etc. [1,2]. For a long time, fractional calculus has been regarded as a pure mathematical realm without real applications. But, in recent decades, such a state of affairs has been changed. It has been found that fraction...

Malliavin calculus and its applications

Fractional Brownian motion: stochastic calculus and applications

Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter H ∈ (0, 1) called the Hurst index. In this note we will survey some facts about the stochastic calculus with respect to fBm using a pathwise approach and the techniques of the Malliavin calculus. Some applications in turbulence and finance will be discussed. Math...