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 …
transforms and Itô integrals, of relevance in rough paths theory, stochastic and harmonic …
Generating diffusions with fractional Brownian motion
We study fast/slow systems driven by a fractional Brownian motion B with Hurst parameter
H∈(1 3, 1]. Surprisingly, the slow dynamic converges on suitable timescales to a limiting …
H∈(1 3, 1]. Surprisingly, the slow dynamic converges on suitable timescales to a limiting …
Time-reversibility and nonvanishing Lévy area
GA Gottwald, I Melbourne - Nonlinearity, 2024 - iopscience.iop.org
We give a complete description and clarification of the structure of the Lévy area correction
to Itô/Stratonovich stochastic integrals arising as limits of time-reversible deterministic …
to Itô/Stratonovich stochastic integrals arising as limits of time-reversible deterministic …
Almost sure diffusion approximation in averaging via rough paths theory
The paper deals with the fast-slow motions setups in the continuous time d X ε (t) dt= 1 ε σ (X
ε (t)) ξ (t∕ ε 2)+ b (X ε (t)), t∈[0, T] and the discrete time XN ((n+ 1)∕ N)= XN (n∕ N)+ N− 1∕ …
ε (t)) ξ (t∕ ε 2)+ b (X ε (t)), t∈[0, T] and the discrete time XN ((n+ 1)∕ N)= XN (n∕ N)+ N− 1∕ …
Periodic homogenisation for
Y Chen, W Xu - arXiv preprint arXiv:2311.16398, 2023 - arxiv.org
arXiv:2311.16398v1 [math.AP] 28 Nov 2023 Periodic homogenisation for P(φ) Page 1 arXiv:2311.16398v1
[math.AP] 28 Nov 2023 Periodic homogenisation for P(φ)2 Yilin Chen Peking University …
[math.AP] 28 Nov 2023 Periodic homogenisation for P(φ)2 Yilin Chen Peking University …
Functional limit theorems for Volterra processes and applications to homogenization
We prove an enhanced limit theorem for additive functionals of a multi-dimensional Volterra
process $(y_t) _ {t\geq 0} $ in the rough path topology. As an application, we establish weak …
process $(y_t) _ {t\geq 0} $ in the rough path topology. As an application, we establish weak …
Periodic homogenisation for two dimensional generalised parabolic Anderson model
Y Chen, B Fehrman, W Xu - arXiv preprint arXiv:2401.05718, 2024 - arxiv.org
We consider the periodic homogenisation problem for the generalised parabolic Anderson
model on two dimensional torus. We show that, for the renormalisation that respects Wick …
model on two dimensional torus. We show that, for the renormalisation that respects Wick …
Nonlinear effects within invariance principles
Functional central limit theorems for random processes viewed as rough paths were
obtained in a wide range of models and settings in recent years. Each result of this kind has …
obtained in a wide range of models and settings in recent years. Each result of this kind has …
Rough invariance principle for delayed regenerative processes
T Orenshtein - Electronic Communications in Probability, 2021 - projecteuclid.org
We derive an invariance principle for the lift to the rough path topology of stochastic
processes with delayed regenerative increments under an optimal moment condition. An …
processes with delayed regenerative increments under an optimal moment condition. An …
Topics in particle systems and singular SDEs
HK Kremp - 2022 - refubium.fu-berlin.de
This thesis studies irregular stochastic (partial) differential equations arising in fluctuating
hydrodynamics or regularization by noise, and homogenization limits thereof. In the first part …
hydrodynamics or regularization by noise, and homogenization limits thereof. In the first part …