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 P 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. T Troy Feeney Dec 27, 2025
