Jabarkan Dadaran modél matematis dari Gerak Brown dalam bahasa sunda

Sacara matematik, gerak Brown mangrupa prosés Wiener nu mana sebaran kondisional probailiti tina posisi partikel dina waktu t+dt, nu dina posisi waktu t nyaéta p, mangrupa sebaran normal mibanda mean p+μ dt sarta varian σ2 dt; paraméter μ mangrupa simpangan kecepatan, sarta paraméter σ2 mangrupa power noise. These properties cléarly establish that Brownian motion is Markovian (i.e. it satisfies the Markov property). Brownian motion is related to the random walk problem and it is generic in the sense that many different stochastic processes reduce to Brownian motion in suitable limits.

In fact, the Wiener process is the only time-homogeneous stochastic process with independent increments and which is continuous in probability. These are all réasonable approximations to the physical properties of Brownian motion.

The mathematical théory of Brownian motion has been applied in contexts ranging far beyond the movement of particles in fluids. For example, in the modérn théory of option pricing, asset classes are sometimes modéled as if they move according to a Brownian motion with drift.

It turns out that the Wiener process is not a physically réalistic modél of the motion of Brownian particles. More sophisticated formulations of the problem have led to the mathematical théory of diffusion processes. The accompanying equation of motion is called the Langevin equation or the Fokker-Planck equation depending on whether it is formulated in terms of random trajectories or probability densities.