Papers, ranked by score

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

Signature SDEs from an affine and polynomial perspective

Signature stochastic differential equations (SDEs) constitute a large class of stochastic processes, here driven by Brownian motions, whose characteristics are linear maps of their own signature, i.e. of iterated integrals of the process with itself, and allow therefore for a generic path dependence

Lab Rats Math 9.5 Rigor 4 ·  February 2, 2023

Stochastic factors can matter: improving robust growth under ergodicity

Drifts of asset returns are notoriously difficult to model accurately and, yet, trading strategies obtained from portfolio optimization are very sensitive to them. To mitigate this well-known phenomenon we study robust growth-optimization in a high-dimensional incomplete market under drift uncertain

Lab Rats Math 8.5 Rigor 3.5 ·  December 31, 2025

Global universal approximation of functional input maps on weighted spaces

We introduce so-called functional input neural networks defined on a possibly infinite dimensional weighted space with values also in a possibly infinite dimensional output space. To this end, we use an additive family to map the input weighted space to the hidden layer, on which a non-linear scalar

Lab Rats Math 9.5 Rigor 1.5 ·  June 5, 2023

Ramifications of generalized Feller theory

Generalized Feller theory provides an important analog to Feller theory beyond locally compact state spaces. This is very useful for solutions of certain stochastic partial differential equations, Markovian lifts of fractional processes, or infinite dimensional affine and polynomial processes which

Lab Rats Math 9.5 Rigor 1 ·  August 7, 2023

Universal approximation property of neural stochastic differential equations

We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neural networks the associated neural stochastic differential equations can approximate general stochastic differential equat

Lab Rats Math 8.5 Rigor 1.5 ·  March 20, 2025

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