Related papers: Neural Jump Stochastic Differential Equations

We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations,…

In this paper, we address the issue of modeling and estimating changes in the state of the spatio-temporal dynamical systems based on a sequence of observations like video frames. Traditional numerical simulation systems depend largely on…

We consider one-dimensional stochastic differential equations with jumps in the general case. We introduce new technics based on local time and we prove new results on pathwise uniqueness and comparison theorems. Our approach are very easy…

In this paper, we study the convergence for solutions to a sequence of (possibly degenerate) stochastic differential equations with jumps, when the coefficients converge in some appropriate sense. Our main tools are the superposition…

We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy…

Predicting discrete events in time and space has many scientific applications, such as predicting hazardous earthquakes and outbreaks of infectious diseases. History-dependent spatio-temporal Hawkes processes are often used to…

This work introduces hybrid stochastic differential equations with memory (mH-SDEs), a new class of stochastic systems where transition rates depend on the joint history of both Euclidean and discrete components. This extends existing…

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…

Neural ordinary differential equations describe how values change in time. This is the reason why they gained importance in modeling sequential data, especially when the observations are made at irregular intervals. In this paper we propose…

Representations of sequential data are commonly based on the assumption that observed sequences are realizations of an unknown underlying stochastic process, where the learning problem includes determination of the model parameters. In this…

The neural Ordinary Differential Equation (ODE) model has shown success in learning complex continuous-time processes from observations on discrete time stamps. In this work, we consider the modeling and forecasting of time series data that…

The Path-Dependent Neural Jump Ordinary Differential Equation (PD-NJ-ODE) is a model for predicting continuous-time stochastic processes with irregular and incomplete observations. In particular, the method learns optimal forecasts given…

Differential equations are used in a wide variety of disciplines, describing the complex behavior of the physical world. Analytic solutions to these equations are often difficult to solve for, limiting our current ability to solve complex…

Stochastic differential equations can describe a wide range of dynamical systems, and obtaining the governing equations of these systems is the premise of studying the nonlinear dynamic behavior of the system. Neural networks are currently…

A multi-type continuous state and continuous time branching process with immigration satisfying some moment conditions is identified as a pathwise unique strong solution of certain stochastic differential equation with jumps.

Recognizing the importance of jump risk in option pricing, we propose a neural jump stochastic differential equation model in this paper, which integrates neural networks as parameter estimators in the conventional jump diffusion model. To…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…

Motivated by the lack of a suitable constructive framework for analyzing popular stochastic models of Systems Biology, we devise conditions for existence and uniqueness of solutions to certain jump stochastic differential equations (SDEs).…

We investigate the existence of a robust, i.e., continuous, representation of the conditional distribution in a stochastic filtering model for multidimensional correlated jump-diffusions. Even in the absence of jumps, it is known that in…

Forecasting system behaviour near and across bifurcations is crucial for identifying potential shifts in dynamical systems. While machine learning has recently been used to learn critical transitions and bifurcation structures from data,…