Awesome SDE(Stochastic Differential Equation)

List of some reference books.

About Stochastic Differential Equation:

1. Applied Stochastic Differential Equations by Simo Särkkä -- Code

2. An introduction to computational Stochastic PDEs by Gabriel J.Lord -- Official Code; Our code Personal code

About Optimal Transport:

1. Optimal Transport for Applied Mathematicians by Filippo Santambrogio

2. Computational Optimal Transport: With Applications to Data Science

3. Optimal Transport by Cedric Villani

About Control theory...

1. An Introduction to Mathematical Optimal Control Theory by Lawrence C. Evans

2. Kalman filter

About Backward stochastic differential equations

1. Nonlinear Expectations, Nonlinear Evaluations and Risk Measures by Peng

2. Backward Stochastic Differential Equations in Finance by N.El Karoui S.Peng and M.C.Quenez

Seminar slides

[18/10/2024] Conditional expectation Brownian motion and stochastic integrals (Guojiang Shao) Video Note

[25/10/2024] Ito formula and SDEs (Guojiang Shao) Video Note

[01/11/2024] Numerical methods for Ito SODEs (Guanyu Chen) Video Note

[09/11/2024] Stationary Process and Random Field (Guanyu Chen) Video Note

[15/11/2024] Introduction to SPDEs and its Numerical methods (Guanyu Chen) Video Note

[22/11/2024] Introduction to Optimal Transport (Yuxuan Shi) Video Note

[29/11/2024] Deterministic optimal control problem (Tianxu Lan) Video Note

[06/12/2024] Introuction of linear filtering problem (Guojiang Shao) Video Note

[13/12/2024] Conservation Laws: Theory and Numerical Methods (Shuang Hu) Video Note: Class Note, Summary(Markdomn)

[20/12/2024] Introduction to BSDEs (Guojiang Shao) Video Note

[27/12/2024] Optimization methods with imagine inverse problems (Shengze Xu)Video Notes

[03/01/2025] SDE and Diffusion Model (Guanyu Chen) Video Note

Paper

[Arxiv 2017] Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

[JMLR 2020] Reinforcement Learning in Continuous Time and Space: A Stochastic Control Approach

[JMLR 2023] q-Learning in Continuous Time

[Arxiv 2022] Stochastic Physics-Informed Neural Ordinary Differential Equations

[University of Calgary 2021] Deep Learning-based Numerical Methods for Stochastic Partial Differential Equations and Applications

[Applied Mathematical Modelling 2023] Neural network stochastic differential equation models with applications to financial data forecasting

[Numerical Algebra, Control and Optimization 2023] Inverse problems for stochastic partial differential equations: Some progresses and open problems

[Journal of Scientific Computing 2022] Solving Stochastic Optimal Control Problem via Stochastic Maximum Principle with Deep Learning Method

[Computers & Graphics]Notions of optimal transport theory and how to implement them on a computer

[AMS Short Course on Discrete Differential Geometry]Optimal Transport on Discrete Domains

[SIAM Journal on Mathematical Analysis]Almost-Sure Stability of the Single Mode Solution of a Noisy Nonlinear Autoparametric System