{"ID":6267025,"CreatedAt":"2026-07-10T01:11:38.759438437Z","UpdatedAt":"2026-07-12T03:44:42.811457357Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.08091","arxiv_id":"2607.08091","title":"Deep Learning Method for Stationary Distribution of Reflected Brownian Motion","abstract":"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. In this paper, we develop 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 careful design of the 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 https://github.com/zhangz73/NN4MGF.","short_abstract":"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 pr...","url_abs":"https://arxiv.org/abs/2607.08091","url_pdf":"https://arxiv.org/pdf/2607.08091v1","authors":"[\"Jim Dai\",\"Zhanhao Zhang\"]","published":"2026-07-09T03:57:12Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[]","has_code":false,"code_links":[{"ID":614071,"CreatedAt":"2026-07-10T01:11:38.759438437Z","UpdatedAt":"2026-07-10T01:11:38.759438437Z","DeletedAt":null,"paper_id":6267025,"paper_url":"https://arxiv.org/abs/2607.08091","paper_title":"Deep Learning Method for Stationary Distribution of Reflected Brownian Motion","repo_url":"https://github.com/zhangz73/NN4MGF","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}