相关论文: Sampling conditioned hypoelliptic diffusions

In this note we provide conditions for local invariance of finite dimensional submanifolds for solutions to stochastic partial differential equations (SPDEs) in the framework of the variational approach. For this purpose, we provide a…

Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate…

We study hypoelliptic stochastic differential equations (SDEs) and their connection to degenerate-elliptic boundary value problems on bounded or unbounded domains. In particular, we provide probabilistic conditions that guarantee that the…

Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function. The accurate estimation (or discovery)…

This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…

This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…

Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…

A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, and…

Let X be the mild solution to a semilinear stochastic partial differential equation. In this article, we develop methodology to sample from the infinite-dimensional diffusion bridge that arises from conditioning X on a linear transformation…

Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…

Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…

This paper presents theoretical advances in the application of the Stochastic Partial Differential Equation (SPDE) approach in geostatistics. We show a general approach to construct stationary models related to a wide class of linear SPDEs,…

Simulating parameter-dependent stochastic differential equations (SDEs) presents significant computational challenges, as separate high-fidelity simulations are typically required for each parameter value of interest. Despite the success of…

In this paper, we are interested in the analytical study of a nonlinear Stochastic Partial Differential Equation (SPDE) arising as a model of phytoplankton aggregation. This SPDE consists in a diffusion equation with a chemotaxis term…

A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…

We investigate a class of stochastic partial differential equations of reaction-diffusion type defined on graphs, which can be derived as the limit of SPDEs on narrow planar channels. In the first part, we demonstrate that this limit can be…

In this study, we introduce a novel method for generating new synthetic samples that are independent and identically distributed (i.i.d.) from high-dimensional real-valued probability distributions, as defined implicitly by a set of Ground…

The Stochastic Partial Differential Equation (SPDE) approach, now commonly used in spatial statistics to construct Gaussian random fields, is revisited from a mechanistic perspective based on the movement of microscopic particles, thereby…

We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…

In this work we investigate the well-posedness for difussion equations associated to subelliptic pseudo-differential operators on compact Lie groups. The diffusion by strongly elliptic operators is considered as a special case and in…