Related papers: A new kind of augmentation of filtrations
In this note we introduce a new kind of augmentation of filtrations along a sequence of stopping times. This augmentation is suitable for the construction of new probability measures associated to a positive strict local martingale as done…
Researchers from different areas have independently defined extensions of the usual weak convergence of laws of stochastic processes with the goal of adequately accounting for the flow of information. Natural approaches are convergence of…
We consider the problem of state estimation in dynamical systems and propose a different mechanism for handling unmodeled system uncertainties. Instead of injecting random process noise, we assign different weights to measurements so that…
With promising empirical performance across a wide range of applications, synthetic data augmentation appears a viable solution to data scarcity and the demands of increasingly data-intensive models. Its effectiveness lies in expanding the…
Traditionally, quantum amplification limit refers to the property of inevitable noise addition on canonical variables when the field amplitude of an unknown state is linearly transformed through a quantum channel. Recent theoretical studies…
In this paper, we introduce the notion of augmentation for polytopes and use it to show the error in two presumptions that have been key in arriving at over-reaching/over-scoped claims of "impossibility" in recent extended formulations (EF)…
A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to…
This paper is on developing stochastic analysis simultaneously under a general family of probability measures that are not dominated by a single probability measure. The interest in this question originates from the probabilistic…
In this paper, we explore various ways in which a factor $\sigma$-algebra $\mathscr{B}$ can sit in a dynamical system $\mathbf{X} :=(X, \mathscr{A}, \mu, T)$, i.e. we study some possible structures of the extension $\mathscr{A} \rightarrow…
Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…
: From the epoch of recombination $(z\approx 10^3)$ till today, the typical density contrasts have grown by a factor of about $10^6$ in a Friedmann universe with $\Omega=1$. However, during the same epoch the typical gravitational potential…
When expanding a filtration with a stochastic process it is easily possible for semimartingale no longer to remain semimartingales in the enlarged filtration. Y. Kchia and P. Protter indicated a way to avoid this pitfall in 2015, but they…
The normalization constraint on probability density poses a significant challenge for solving the Fokker-Planck equation. Normalizing Flow, an invertible generative model leverages the change of variables formula to ensure probability…
We consider a complete probability space $(\Omega,\mathcal{F},\mathbb{P})$, which is endowed with two filtrations, $\mathbb{G}$ and $\mathbb{F}$, assumed to satisfy the usual conditions and such that $\mathbb{F} \subset \mathbb{G}$. On this…
Using a method of eigenfunction expansion, a stochastic equation is developed for the generalized Schr{\"o}dinger equation with random fluctuations. The wave field $ {\psi} $ is expanded in terms of eigenfunctions: $ {\psi} = \sum_{n} a_{n}…
The Wiener Sausage, the volume traced out by a sphere attached to a Brownian particle, is a classical problem in statistics and mathematical physics. Initially motivated by a range of field-theoretic, technical questions, we present a…
Incremental flow-based denoising models have reshaped generative modelling, but their empirical advantage still lacks a rigorous approximation-theoretic foundation. We show that incremental generation is necessary and sufficient for…
Wasserstein distance induces a natural Riemannian structure for the probabilities on the Euclidean space. This insight of classical transport theory is fundamental for tremendous applications in various fields of pure and applied…
In this paper, we describe a novel application of sigma-point methods to continuous-discrete filtering. In principle, the nonlinear continuous- discrete filtering problem can be solved exactly. In practice, the solution contains terms that…
Let $\Omega\subset\mathbb{R}^n$ be an open, connected subset of $\mathbb{R}^n$, and let $F\colon\Omega-\Omega\to\mathbb{C}$, where $\Omega-\Omega=\{x-y\colon x,y\in\Omega\}$, be a continuous positive definite function. We give necessary and…