Related papers: Practical Estimation of High Dimensional Stochasti…

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…

Stochastic Differential Equations (SDEs) are used as statistical models in many disciplines. However, intractable likelihood functions for SDEs make inference challenging, and we need to resort to simulation-based techniques to estimate and…

This paper considers estimating the parameters in a regime-switching stochastic differential equation(SDE) driven by Normal Inverse Gaussian(NIG) noise. The model under consideration incorporates a continuous-time finite state Markov chain…

Understanding sustainability through modeling involves one of the complex and interdisciplinary activities where mathematics plays a key role. We provide arguments favoring the need for developing global models for measuring the status of…

Parameters of the mathematical model describing many practical dynamical systems are prone to vary due to aging or renewal, wear and tear, as well as changes in environmental or service conditions. These variabilities will adversely affect…

Research on asymptotic model selection in the context of stochastic differential equations (SDEs) is almost non-existent in the literature. In particular, when a collection of SDEs is considered, the problem of asymptotic model selection…

In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…

Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary…

Astronomical time series from large-scale surveys like LSST are often irregularly sampled and incomplete, posing challenges for classification and anomaly detection. We introduce a new framework based on Neural Stochastic Delay Differential…

The hazard function represents one of the main quantities of interest in the analysis of survival data. We propose a general approach for parametrically modelling the dynamics of the hazard function using systems of autonomous ordinary…

Traditional deterministic subgrid-scale (SGS) models are often dissipative and unstable, especially in regions of chaotic and turbulent flow. Ongoing work in climate science and ocean modeling motivates the use of stochastic SGS models for…

Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…

Intrinsically noisy mechanisms drive most physical, biological and economic phenomena, from stock pricing to phenotypic variability. Frequently, the system's state influences the driving noise intensity, as, for example, the actual value of…

This paper investigates a class of controlled stochastic partial differential equations (SPDEs) arising in the modeling of composite materials with spatially varying properties. The state equation describes the evolution of a material…

Considering generating samples with high rewards, we focus on optimizing deep neural networks parameterized stochastic differential equations (SDEs), the advanced generative models with high expressiveness, with policy gradient, the leading…

The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions.…

Mathematical modeling with Ordinary Differential Equations (ODEs) has proven to be extremely successful in a variety of fields, including biology. However, these models are completely deterministic given a certain set of initial conditions.…

The paper investigates existence and uniqueness for a stochastic differential equation (SDE) with distributional drift depending on the law density of the solution. Those equations are known as McKean SDEs. The McKean SDE is interpreted in…

Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even…

This paper addresses the problem of estimating the modes of an observed non-stationary mixture signal in the presence of an arbitrary distributed noise. A novel Bayesian model is introduced to estimate the model parameters from the…