Related papers: Neural Jump Stochastic Differential Equations
Stochastic dual dynamic programming (SDDP) is a state-of-the-art method for solving multi-stage stochastic optimization, widely used for modeling real-world process optimization tasks. Unfortunately, SDDP has a worst-case complexity that…
Despite the striking successes of deep neural networks trained with gradient-based optimization, these methods differ fundamentally from their biological counterparts. This gap raises key questions about how nature achieves robust,…
In this paper, we investigate stochastic continuity (with respect to the initial value), irreducibility and non confluence property of the solutions of stochastic differential equations with jumps. The conditions we posed are weaker than…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
Using neural networks to solve partial differential equations (PDEs) is gaining popularity as an alternative approach in the scientific computing community. Neural networks can integrate different types of information into the loss…
We explicitly construct so-called captive jump processes. These are stochastic processes in continuous time, whose dynamics are confined by a time-inhomogeneous bounded domain. The drift and volatility of the captive processes depend on the…
Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…
This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
Unlike in the traditional statistical modeling for which a user typically hand-specify a prior, Neural Processes (NPs) implicitly define a broad class of stochastic processes with neural networks. Given a data stream, NP learns a stochastic…
Stochastic dynamics of several systems can be modeled via piecewise deterministic time evolution of the state, interspersed by random discrete events. Within this general class of systems, we consider time-triggered stochastic hybrid…
We consider the modeling of the dynamics of the chemostat at its very source. The chemostat is classically represented as a system of ordinary differential equations. Our goal is to establish a stochastic model that is valid at the scale…
We consider a stochastic version of the point vortex system, in which the fluid velocity advects single vortices intermittently for small random times. Such system converges to the deterministic point vortex dynamics as the rate at which…
Stochastic processes generated by non-stationary distributions are difficult to represent with conventional models such as Gaussian processes. This work presents Recurrent Autoregressive Flows as a method toward general stochastic process…
We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
Perception of time from sequentially acquired sensory inputs is rooted in everyday behaviors of individual organisms. Yet, most algorithms for time-series modeling fail to learn dynamics of random event timings directly from visual or audio…
Accurate crowd simulation is crucial for public safety management, emergency evacuation planning, and intelligent transportation systems. However, existing methods, which typically model crowds as a collection of independent individual…
Clinical time series data from electronic health records and medical registries offer unprecedented opportunities to understand patient trajectories and inform medical decision-making. However, leveraging such data presents significant…