Related papers: Most probable paths for developed processes
In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…
We propose a novel stochastic method to exactly generate Brownian paths conditioned to start at an initial point and end at a given final point during a fixed time $t_{f}$. These paths are weighted with a probability given by the overdamped…
For sub-Riemannian manifolds with a chosen complement, we first establish the derivative formula and integration by parts formula on path space with respect to a natural gradient operator. By using these formulae, we then show that upper…
Optimal transport is a geometrically intuitive, robust and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This…
This paper considers maximum likelihood inference for a functional marked point process - the stochastic growth-interaction process - which is an extension of the spatio-temporal growth-interaction process to the stochastic mark setting. As…
Flow matching trains a neural velocity field by regression against a target velocity associated with a prescribed probability path connecting a simple initial distribution to the data distribution. A central design choice is the path…
Considering the paradigmatic driven Brownian motion, we perform extensive numerical analysis on the performance of optimal linear-response processes far from equilibrium. We focus on the overdamped regime where exact optimal processes are…
The Ornstein-Uhlenbeck process is interpreted as Brownian motion in a harmonic potential. This Gaussian Markov process has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. It…
Flip-flop processes refer to a family of stochastic fluid processes which converge to either a standard Brownian motion (SBM) or to a Markov modulated Brownian motion (MMBM). In recent years, it has been shown that complex distributional…
Effective movement primitives should be capable of encoding and generating a rich repertoire of trajectories -- typically collected from human demonstrations -- conditioned on task-defining parameters such as vision or language inputs.…
We study an ancient problem that in a static or dynamical system, sought an optimal path, which the context always means within an extremal condition. In fact, through those discussions about this theme, we established a universal essential…
We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation…
Consider a d-dimensional Brownian motion in a random potential defined by attaching a nonnegative and polynomially decaying potential around Poisson points. We introduce a repulsive interaction between the Brownian path and the Poisson…
This work puts forth low-complexity Riemannian subspace descent algorithms for the minimization of functions over the symmetric positive definite (SPD) manifold. Different from the existing Riemannian gradient descent variants, the proposed…
Gaussian processes are used in many machine learning applications that rely on uncertainty quantification. Recently, computational tools for working with these models in geometric settings, such as when inputs lie on a Riemannian manifold,…
We present an alternative to the perturbative diagrammatic approach for studying stochastic dynamics. Our approach is based on an auxiliary field loop expansion for the path integral representation for the generating functional of the noise…
The Ornstein-Uhlenbeck process can be seen as a paradigm of a finite-variance and statistically stationary rough random walk. Furthermore, it is defined as the unique solution of a Markovian stochastic dynamics and shares the same local…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
The probability current is a vital quantity in the Fokker-Planck description of stochastic processes. It characterizes non-equilibrium stationary states and appears in linear response calculations. We recover and review the probability…
Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on…