[ספר][B] A course on rough paths

PK Friz, M Hairer - 2020‏ - Springer
Peter K. Friz Martin Hairer With an Introduction to Regularity Structures Second Edition
Page 1 Universitext Peter K. Friz Martin Hairer A Course on Rough Paths With an …

Signature methods in machine learning

T Lyons, AD McLeod - arxiv preprint arxiv:2206.14674, 2022‏ - arxiv.org
Signature-based techniques give mathematical insight into the interactions between
complex streams of evolving data. These insights can be quite naturally translated into …

Rough stochastic differential equations

PK Friz, A Hocquet, K Lê - arxiv preprint arxiv:2106.10340, 2021‏ - arxiv.org
We establish a simultaneous generalization of It\^ o's theory of stochastic and Lyons' theory
of rough differential equations. The interest in such a unification comes from a variety of …

Averaging principle for fast-slow system driven by mixed fractional Brownian rough path

B Pei, Y Inahama, Y Xu - Journal of Differential Equations, 2021‏ - Elsevier
This paper is devoted to studying the averaging principle for a fast-slow system of rough
differential equations driven by mixed fractional Brownian rough path. The fast component is …

Robust filtering: correlated noise and multidimensional observation

D Crisan, J Diehl, PK Friz, H Oberhauser - 2013‏ - projecteuclid.org
In the late seventies, Clark In Communication Systems and Random Process Theory (Proc.
2nd NATO Advanced Study Inst., Darlington, 1977)(1978) 721–734, Sijthoff & Noordhoff …

The Jain–Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory

PK Friz, B Gess, A Gulisashvili, S Riedel - 2016‏ - projecteuclid.org
We discuss stochastic calculus for large classes of Gaussian processes, based on rough
path analysis. Our key condition is a covariance measure structure combined with a …

Stochastic partial differential equations: a rough paths view on weak solutions via Feynman–Kac

J Diehl, PK Friz, W Stannat - Annales de la Faculté des …, 2017‏ - afst.centre-mersenne.org
We discuss regular and weak solutions to rough partial differential equations (RPDEs),
thereby providing a (rough path-) wise view on important classes of SPDEs. In contrast to …

Solving mean field rough differential equations

I Bailleul, R Catellier, F Delarue - 2020‏ - projecteuclid.org
We provide in this work a robust solution theory for random rough differential equations of
mean field type dX_t=V\big(X_t,\mathcalL(X_t)\big)dt+F\bigl(X_t,\mathcalL(X_t)\bigr)dW_t …

Rough PDEs for local stochastic volatility models

P Bank, C Bayer, PK Friz, L Pelizzari - Mathematical Finance, 2023‏ - Wiley Online Library
In this work, we introduce a novel pricing methodology in general, possibly non‐Markovian
local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics …

Rough semimartingales and p-variation estimates for martingale transforms

PK Friz, P Zorin-Kranich - The Annals of Probability, 2023‏ - projecteuclid.org
We establish a new scale of p-variation estimates for martingale paraproducts, martingale
transforms and Itô integrals, of relevance in rough paths theory, stochastic and harmonic …