We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization
on the space of probability measures, with Kullback–Leibler (KL) divergence as the …

Motivated by the occurrence in rate functions of time-dependent large-deviation principles,
we study a class of non-negative functions ℒ that induce a flow, given by ℒ (ρ t, ρ ̇ t)= 0 …

In this article, we study the Schrödinger bridge problem (SBP) with nonlinear prior dynamics.
In control-theoretic language, this is a problem of minimum effort steering of a given joint …

We develop a new computational framework to solve the partial differential equations
(PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time …

In this paper we present a variational technique that handles coarse-graining and passing to
a limit in a unified manner. The technique is based on a duality structure, which is present in …

In this paper, we study the set of stationary solutions of the Vlasov–Fokker–Planck (VFP)
equation. This equation describes the time evolution of the probability distribution of a …

We consider three one-dimensional continuous-time Markov processes on a lattice, each of
which models the conduction of heat: the family of Brownian Energy Processes with …

We present a proximal algorithm that performs a variational recursion on the space of joint
probability measures to propagate the stochastic uncertainties in power system dynamics …

In this paper, we develop a natural operator-splitting variational scheme for a general class
of non-local, degenerate conservative-dissipative evolutionary equations. The splitting …

In this work, we investigate a variational formulation for a time-fractional Fokker-Planck
equation which arises in the study of complex physical systems involving anomalously slow …