The stationary distribution of reflected Brownian motion (RBM) plays an important role in the analysis of high-dimensional stochastic systems, yet closed-form solutions are known only for a few special cases. Computing important performance metrics, such as tail probabilities, is even more intractable, despite their practical relevance. This paper develops a deep learning approach that accurately and efficiently learns the Laplace transform of high-dimensional RBMs based on the basic adjoint relationship (BAR).
Our framework combines a carefully designed loss function, training data sampling procedure, and neural network architecture. We evaluate the proposed method on RBM instances with known ground-truth tail probabilities and demonstrate near-perfect prediction in high-dimensional settings, highlighting its potential as a general tool for analyzing stochastic systems beyond analytically tractable regimes.
Our code can be found at: GitHub Repository.
Blogger's Review: This research showcases the potential of deep learning in tackling complex stochastic systems, providing a new tool to address problems that traditional methods cannot solve analytically. Its open-source code also facilitates further research and application in fields like finance and physics.