Related papers: Using coupling methods to estimate sample quality …
Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
The efficient simulation of the mean value of a non-linear functional of the solution to a linear stochastic partial differential equation (SPDE) with additive Gaussian noise is considered. A Galerkin finite element method is employed along…
The probability density function (PDF) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a truncated series expansion. The random PDE is solved using two…
In this paper, we propose a chance constrained stochastic model predictive control scheme for reference tracking of distributed linear time-invariant systems with additive stochastic uncertainty. The chance constraints are reformulated…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
We introduce and test methods for the calibration of the diffusion term in Stochastic Partial Differential Equations (SPDEs) describing fluids. We take two approaches, one uses ideas from the singular value decomposition and the Biot-Savart…
This paper presents a new stochastic finite element method for computing structural stochastic responses. The method provides a new expansion of stochastic response and decouples the stochastic response into a combination of a series of…
While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…
This paper deals with the Monte-Carlo methods for evaluating expectations of functionals of solutions to McKean-Vlasov Stochastic Differential Equations (MV-SDE) with drifts of super-linear growth. We assume that the MV-SDE is approximated…
Sampling algorithms play a pivotal role in probabilistic AI. However, verifying if a sampler program indeed samples from the claimed distribution is a notoriously hard problem. Provably correct testers like Barbarik, Teq, Flash, CubeProbe…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee…
We propose a coupled rejection-sampling method for sampling from couplings of arbitrary distributions. The method relies on accepting or rejecting coupled samples coming from dominating marginals. Contrary to existing acceptance-rejection…
Generalizing an idea of Davie and Gaines (2001), we present a method for the simulation of fully discrete samples of the solution to the stochastic heat equation on an interval. We provide a condition for the validity of the approximation,…
This paper presents a new approach to statistical similarity assessment based on sequence alignment. The algorithm performs mutual matching of two random sequences by successively searching for common elements and by applying sequence…
This paper focuses on the numerical scheme for multiple-delay stochastic differential equations with partially H\"older continuous drifts and locally H\"older continuous diffusion coefficients. To handle with the superlinear terms in…
In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…