This paper presents the multivariable extension of the feedback particle filter (FPF) algorithm
for the nonlinear filtering problem in continuous-time. The FPF is a control-oriented …

We study interacting systems of linear Brownian motions whose drift vector at every time
point is determined by the relative ranks of the coordinate processes at that time. Our main …

We determine rates of convergence of rank-based interacting diffusions and semimartingale
reflecting Brownian motions to equilibrium. Bounds on fluctuations of additive functionals are …

A new class of particle systems with sequential interaction is proposed to approximate the
McKean-Vlasov process that originally arises as the limit of the mean-field interacting …

Consider a time-varying collection of n points on the positive real axis, modeled as
Exponentials of n Brownian motions whose drift vector at every time point is determined by …

Consider a system of infinitely many Brownian particles on the real line. At any moment,
these particles can be ranked from the bottom upward. Each particle moves as a Brownian …

Consider the infinite Atlas model: a semi-infinite collection of particles driven by independent
standard Brownian motions with zero drifts, except for the bottom-ranked particle which …