Integrability of (Non-)Linear Rough Differential Equations and Integrals

By Peter K. Friz. 2011

52 citations recorded by the source corpus.

Integrability properties of (classical, linear, linear growth) rough differential equations (RDEs) are considered, the Jacobian of the RDE flow driven by Gaussian signals being a motivating example. We revisit and extend some recent ground-breaking work of Cass-Litterer-Lyons in this regard; as by-product, we obtain a user-friendly “transitivity property” of such integrability estimates. We also consider rough integrals; as a novel application, uniform Weibull tail estimates for a class of (random) rough integrals are obtained. A concrete example arises from the stochastic heat-equation, spatially mollified by hyper-viscosity, and we can recover (in fact, sharpen) a technical key result of Hairer [11].

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cb9a8f93206e0562aaee3759847160fafa44709a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Archil Gulisashvili
2. Benjamin Gess
3. Peter K. Friz
4. Nicolas Victoir
5. Samy Tindel
6. T. Cass
7. Martin Hairer
8. Wei Liu

In Global and Planetary Change

1. Archil Gulisashvili
2. Benjamin Gess

In Statistics and Probability

1. Archil Gulisashvili
2. Benjamin Gess
3. Peter K. Friz
4. Martin Hairer

Citations in the corpus

• The Jain–Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory (2013, background): “3Such integrability properties can be crucial in SPDE theory [10, 14, 22] and in robust filtering theory [7, 11].”