Stochastic Integration Techniques

 Stochastic Integration Techniques:

Generalization of the classical Riemann-Stieltjes integral. Integrals where the integrator is a continuous martingale

Brownian Motion:

Brownian motion is the macroscopic picture emerging from a particle moving randomly in d-dimensional space. On the microscopic level, at any time step, the particle receives a random displacement, caused for example by other particles hitting it or by an external force.

A geometric Brownian motion is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion.

Stochastic (Martingale):

 Martingale-

Martingales are a class of real-valued stochastic processes in discrete time: Brownian Motion, Brownian Motion with drift, Wald’s martingale.

Properties:

Stochastic Calculs Important Formula's