Related papers: A control variate method driven by diffusion appro…
Accurate quantification of safety is essential for the design of autonomous systems. In this paper, we present a methodology to characterize the exact probabilities associated with invariance and recovery in safe control. We consider a…
Estimation and inference procedures for synthetic control methods often do not allow for the existence of spillover effects, which are plausible in many applications. In this paper, we consider estimation and inference for synthetic control…
We consider the problem of estimating the mean of a random vector based on $N$ independent, identically distributed observations. We prove the existence of an estimator that has a near-optimal error in all directions in which the variance…
We present two limit theorems, a mean ergodic and a central limit theorem, for a specific class of one-dimensional diffusion processes that depend on a small-scale parameter $\varepsilon$ and converge weakly to a homogenized diffusion…
We show a probabilistic functional limit result for one-dimensional diffusion processes that are reflected at an elastic boundary which is a function of the reflection local time. Such processes are constructed as limits of a sequence of…
This work introduces a new approximate proximal sampler that operates solely with zeroth-order information of the potential function. Prior theoretical analyses have revealed that proximal sampling corresponds to alternating forward and…
The main result in this paper is a variational formula for the exit rate from a bounded domain for a diffusion process in terms of the stationary law of the diffusion constrained to remain in this domain forever. Related results on the…
The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs.…
Motivated in part by a problem in simulated tempering (a form of Markov chain Monte Carlo) we seek to minimise, in a suitable sense, the time it takes a (regular) diffusion with instantaneous reflection at 0 and 1 to travel to $1$ and then…
Autocorrelations in MCMC chains increase the variance of the estimators they produce. We propose the occlusion process to mitigate this problem. It is a process that sits upon an existing MCMC sampler, and occasionally replaces its samples…
This paper continues the examination of inventory control in which the inventory is modelled by a diffusion process and a long-term average cost criterion is used to make decisions. The class of such models under consideration have general…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and…
Diffusion models have become popular for policy learning in robotics due to their ability to capture high-dimensional and multimodal distributions. However, diffusion policies are stochastic and typically trained offline, limiting their…
The numerical approximation of posterior expected quantities of interest is considered. A novel control variate technique is proposed for post-processing of Markov chain Monte Carlo output, based both on Stein's method and an approach to…
We propose $\textit{iterative inversion}$ -- an algorithm for learning an inverse function without input-output pairs, but only with samples from the desired output distribution and access to the forward function. The key challenge is a…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
We consider the nonlinear optimal control of bypass transition in a boundary layer flow subjected to a pair of free stream vortical perturbations using a receding horizon approach. The optimal control problem is solved using the Lagrange…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
We introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In…