The field of stochastic dynamics is moving towards the development of more accurate and efficient numerical methods for solving complex stochastic differential equations. Recent research has focused on improving the accuracy and stability of existing methods, such as the Euler-Maruyama method, and developing new methods that can handle high-dimensional systems and non-Gaussian distributions. Notable developments include the introduction of new numerical schemes for solving the Fokker-Planck equation and the development of more efficient algorithms for estimating parameters in stochastic models. Additionally, there is a growing interest in applying stochastic dynamics to real-world problems, such as modeling the spread of diseases and understanding complex systems. Some notable papers in this area include the development of a new class of numerical methods for solving stochastic differential equations on Riemannian manifolds, a novel numerical scheme for solving the Fokker-Planck equation of discretized Dean-Kawasaki models, and a data assimilation strategy for accurately capturing key non-Gaussian structures in probability distributions. Overall, the field is seeing significant innovations in numerical methods and applications, with a focus on improving accuracy, efficiency, and robustness.
Advances in Stochastic Dynamics and Numerical Methods
Sources
High order integration of stochastic dynamics on Riemannian manifolds with frozen flow methods
Solving the Fokker-Planck equation of discretized Dean-Kawasaki models with functional hierarchical tensor
Data Assimilation Models for Computing Probability Distributions of Complex Multiscale Systems
Bayesian Inference for a Time-Fractional HIV Model with Nonlinear Diffusion
Beyond Gaussian Assumptions: A Nonlinear Generalization of Linear Inverse Modeling
Matching random colored points with rectangles (Corrigendum)
Explorable INR: An Implicit Neural Representation for Ensemble Simulation Enabling Efficient Spatial and Parameter Exploration
Efficient State Estimation of a Networked FlipIt Model
The optimal strong convergence rates of the truncated EM and logarithmic truncated EM methods for multi-dimensional nonlinear stochastic differential equations
Hidden Markov Model Filtering with Equal Exit Probabilities
Multi-fidelity Parameter Estimation Using Conditional Diffusion Models
A Unified Approach to Analysis and Design of Denoising Markov Models
Enhanced Diffusion Sampling via Extrapolation with Multiple ODE Solutions
Stochastic positivity-preserving symplectic splitting methods for stochastic Lotka--Volterra predator-prey model
Variational Online Mirror Descent for Robust Learning in Schr\"odinger Bridge
Convergence of the Markovian iteration for coupled FBSDEs via a differentiation approach