Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

A high-order recombination algorithm with adaptive scale selection for weak approximation of stochastic differential equations

High-order recombination keeps weak approximation trees of diffusions small by a moment-preserving reduction of the measure on each patch of nodes. The weighted Litterer–Lyons (WLL) test of Ninomiya and Shinozaki sets the patch scale using a scalar \(λ>0\) chosen beforehand, whose appropriate value

Holy Grail Math 9 Rigor 6 ·  November 11, 2026

A new architecture of high-order deep neural networks that learn martingales

A new deep-learning neural network architecture based on high-order weak approximation algorithms for stochastic differential equations (SDEs) is proposed. The architecture enables the efficient learning of martingales by deep learning models. The behaviour of deep neural networks based on this arch

Lab Rats Math 8.5 Rigor 4 ·  May 1, 2025

A high-order recombination algorithm for weak approximation of stochastic differential equations

This paper presents an algorithm for applying the high-order recombination method, originally introduced by Lyons and Litterer in ``High-order recombination and an application to cubature on Wiener space’’ (Ann. Appl. Probab. 22(4):1301–1327, 2012), to practical problems in mathematical finance. A r

Lab Rats Math 9.5 Rigor 3 ·  April 28, 2025

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