Evolution Of The Position Of A Particle SDE

Available identifiers

MaRDI QIDQ6775463

positions of particles evolve according to this set of coupled SDEs

Description

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

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Defining Formula: $d{X}_i(t)=-\frac{1}{N}\sum _{j=1}^N{F}^{\prime }(X_i(t)-X_j(t))dt+\sigma d{W}_i(t)$

$F(x)$ symbol represents Interaction Potential

$N$ symbol represents Number of Particles

$W_i$ symbol represents Wiener Process

$X_i$ symbol represents Position Of A Particle

$\sigma$ symbol represents Diffusion Coefficient

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