A Course on Rough Paths: With an Introduction to Regularity Structures

By Peter K. Friz, Martin Hairer. 2014

379 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/102e9d0cee1b63458b612197a515942b4f116b00

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Citations in the corpus

HIGH ORDER PARACONTROLLED CALCULUS (2016, background): “´ dq´-truly rough. A suﬃcient condition for a function for being truly rough is provided by Hairer-Pillai’s notion of θ-rough function [21]; see for instance section 6.4 of FrizHairer’s lecture notes [11]. It may be interesting to note that Norris lemma holds in that case, giving a control of the L8”
Noiseless regularisation by noise (2020, unknown): “24 from [28]) JθKCγ .”
Discretely sampled signals and the rough Hoff process (2013, background): “For a more detailed overview of the theory we direct the reader to [8, 11, 16, 18, 20, 22] among many others.”
The Jain–Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory (2013, background): “also [19]) to construct a (random) rough path X associated to X.”
Pathwise stochastic integrals for model free finance (2013, methodology): “The main difference to [19] in the derivation below is that we use p-variation to describe the regularity, and not Hölder continuity,”
A regularity structure for rough volatility (2017, methodology): “In the theory of rough paths, one usually takes 𝜑(𝑡) = 𝟏[𝑠,𝑡′](𝑡) for 𝑠 𝑡′ (see also P. K. Friz & Hairer, 2014, Section 13.3.2), which explains why issues of this kind never arise in the rough path framework.”
Canonical RDEs and general semimartingales as rough paths (2017, background): “The important operation of translating rough paths in some h-direction, formally ∫ (x + h) ⊗ d(x + h), can be algebraically formulated in terms of the Young pairing and has found many applications [18].”
General Rough integration, Levy Rough paths and a Levy--Kintchine type formula (2012, methodology): “(The situation can be compared with [14], Section 4.”
A priori estimates for rough PDEs with application to rough conservation laws (2016, background): “• Mild formulation of rough Burgers equations with spatially irregular noise have been first introduced by Hairer and Weber [38,39] and Hairer, Maas and Weber [37] leading to the groundbreaking work of Hairer on the Kardar–Parisi–Zhang equation [35].”
Averaging principle for fast-slow system driven by mixed fractional Brownian rough path (2020, methodology): “βkv − ˜vk 2β,∆a,b. 2.2 Rough paths theory with approximation by Riemann sums In this subsection, we write a β-Ho¨lder rough path by (X,X2) instead of (ω,ω2) following the notations by Friz and Hairer [9]. Deﬁnition 2.9. We say that a pair (x,x†) is a controlled path with respect to (X,X2) if the fol”
Characteristic functions of measures on geometric rough paths (2013, background): “e the sequence of times τ0 = 0, τj+1 = inf{t > τj |ω x(τj,t) ≥α}∧T, so that ω x(τj,τj+1) = α for all 0 ≤j < N = Nα,[0,T],p(x) := sup{k ≥0 |τj < T} and ω x(τN,τN+1) ≤1 (see [4] Deﬁnition 4.7, [10] p.158). Note that evidently np(x) ≤N1,[0,T],p(x) +1. Let Np(V ) be the family of GΩp-valued ran”