#brownian

shreve brownian motion and stochastic calculus

framework. Introduction to Brownian Motion What is Brownian Motion? Brownian motion, named after the botanist Robert Brown, describes the random, erratic motion of particles suspended in a fluid. Mathematically, it is modeled as a continuo

Patty Rippin • Nov 20, 2025

brownian motion martingales and stochastic calcul

ifically, for a Brownian filtration, every martingale \( M_t \) admits a representation: \[ M_t = M_0 + \int_0^t \phi_s \, dB_s \] where \( \phi_s \) is an adapted process satisfying integrability conditions.

Troy Feeney • Dec 27, 2025