Evolution Of The Position Of A Particle SDE

Available identifiers

positions of particles evolve according to this set of coupled SDEs

𝑋(𝑡) = (𝑋₁(𝑡), …, 𝑋ₙ(𝑡)) denote the (random) system state at time 𝑡

Defining Formula: $d X_{i} (t) = - \frac{1}{N} \sum_{j = 1}^{N} F^{'} (X_{i} (t) - X_{j} (t)) d t + σ d W_{i} (t)$
$F (x)$ symbol represents Interaction Potential
$N$ symbol represents Number of Particles
$W_{i}$ symbol represents Wiener Process
$X_{i}$ symbol represents Position Of A Particle
$σ$ symbol represents Diffusion Coefficient