Motivated by the paradigm of reservoir computing, we consider randomly initialized
controlled ResNets defined as Euler-discretizations of neural controlled differential …

This work studies approximation based on single-hidden-layer feedforward and recurrent
neural networks with randomly generated internal weights. These methods, in which only …

We consider a stochastic volatility model where the dynamics of the volatility are described
by a linear function of the (time extended) signature of a primary process which is supposed …

We consider asset price models whose dynamics are described by linear functions of the
(time extended) signature of a primary underlying process, which can range from a (market …

Deep neural networks based on linear RNNs interleaved with position-wise MLPs are
gaining traction as competitive approaches for sequence modeling. Examples of such …

Reservoir computing approximation and generalization bounds are proved for a new
concept class of input/output systems that extends the so-called generalized Barron …

In the context of stochastic portfolio theory we introduce a novel class of portfolios which we
call linear path-functional portfolios. These are portfolios which are determined by certain …

A universal kernel is constructed whose sections approximate any causal and time-invariant
filter in the fading memory category with inputs and outputs in a finite-dimensional Euclidean …

Many finance, physics, and engineering phenomena are modeled by continuous-time
dynamical systems driven by highly irregular (stochastic) inputs. A powerful tool to perform …

Using short histories of observations from a dynamical system, a workflow for the post-
training initialization of reservoir computing systems is described. This strategy is called cold …