State spaces of multifactor approximations of nonnegative Volterra processes

TL;DR

This paper characterizes the state spaces of multifactor Markovian approximations of nonnegative Volterra processes, providing explicit linear transformations of the nonnegative orthant, which aids in simulation and PDE applications.

Contribution

It introduces an explicit linear transformation framework for the state spaces of multifactor Markovian approximations of nonnegative Volterra processes, enhancing practical computational methods.

Findings

State spaces are explicit linear transformations of the nonnegative orthant.

The results facilitate simulation schemes for nonnegative Volterra processes.

The approach improves PDE-based methods for these processes.

Abstract

We show that the state spaces of multifactor Markovian processes, coming from approximations of nonnegative Volterra processes, are given by explicit linear transformation of the nonnegative orthant. We demonstrate the usefulness of this result for applications, including simulation schemes and PDE methods for nonnegative Volterra processes.