arXiv:2607.08091v1 Announce Type: new 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 care
The continuous advancements in deep learning methodologies enable new approaches to complex stochastic problems that were previously intractable with closed-form solutions.
This development represents a new computational tool for modeling high-dimensional stochastic systems, potentially improving performance metrics and predictions in critical applications.
The ability to accurately and efficiently learn stationary distributions of RBMs using deep learning could refine analyses in fields like queueing theory or financial modeling where such systems are prevalent.
- · AI researchers in stochastic processes
- · Financial modeling sector
- · Logistics and operations research
More accurate simulations and predictions for systems involving reflected Brownian motion become feasible.
Improved efficiency in designing systems that rely on understanding these complex stochastic behaviors, potentially leading to better risk management or resource allocation.
The methodology could be extended to other, even more complex, non-linear stochastic systems, accelerating AI deployment in new scientific and engineering domains.
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Read at arXiv cs.LG