A continuous-time stochastic process B_t with B_0=0, independent increments, B_t−B_s ∼ N(0, t−s), and continuous sample paths. Canonical example of a continuous martingale.
Brownian motion (Wiener process)
Related concepts
- Gaussian (normal) distribution
- Martingale
- Itô integral
- Kolmogorov probability axioms
- Langevin equation
- Quantum Monte Carlo
- Stokes-Einstein framework: D = k_B·T/(6πηR) (Brownian diffusion of a sphere in viscous fluid)
- Drift-diffusion model (DDM): dx = v·dt + dW_t; absorbing barriers ±a/2; ⟨T⟩=(a/2v)·tanh(av/2)