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 …

Genetic Algorithms (GA) are a class of metaheuristic global optimization methods inspired
by the process of natural selection among individuals in a population. Despite their …

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 …

We study a quasilinear parabolic Cauchy problem with a cumulative distribution function on
the real line as an initial condition. We call 'probabilistic solution'a weak solution which …

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

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 …

We study the diffusion of N particles in one dimension interacting via a drift proportional to
their rank. In the attractive case (self-gravitating gas) a mapping to the Lieb-Liniger quantum …

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 …

The mean-field limit of a Markovian model describing the interaction of several classes of
permanent connections in a network is analyzed. Each of the connections has a self …