Invariance principle via orthomartingale approximation
D Giraudo - Stochastics and Dynamics, 2018 - World Scientific
We obtain a necessary and sufficient condition for the orthomartingale-coboundary
decomposition. We establish a sufficient condition for the approximation of the partial sums …
decomposition. We establish a sufficient condition for the approximation of the partial sums …
Moment inequalities for sums of weakly dependent random fields
G Blanchard, A Carpentier, O Zadorozhnyi - Bernoulli, 2024 - projecteuclid.org
Abstract We derive both Azuma-Hoeffding and Burkholder-type inequalities for partial sums
over a rectangular grid of dimension d of a random field satisfying a weak dependency …
over a rectangular grid of dimension d of a random field satisfying a weak dependency …
Quenched invariance principles for orthomartingale-like sequences
M Peligrad, D Volný - Journal of Theoretical Probability, 2020 - Springer
In this paper, we study the central limit theorem and its functional form for random fields
which are started not from their equilibrium, but rather under the measure conditioned by the …
which are started not from their equilibrium, but rather under the measure conditioned by the …
[HTML][HTML] Limit theorems for weighted Bernoulli random fields under Hannan's condition
J Klicnarová, D Volný, Y Wang - Stochastic Processes and their …, 2016 - Elsevier
Recently, invariance principles for partial sums of Bernoulli random fields over rectangular
index sets have been proved under Hannan's condition. In this note we complement …
index sets have been proved under Hannan's condition. In this note we complement …
Martingale-coboundary representation for stationary random fields
D Volný - Stochastics and Dynamics, 2018 - World Scientific
We prove a martingale-coboundary representation for random fields with a completely
commuting filtration. For random variables in L 2, we present a necessary and sufficient …
commuting filtration. For random variables in L 2, we present a necessary and sufficient …
[PDF][PDF] Double coboundaries for commuting contractions
Let T and S be commuting contractions on a Banach space X. We consider the problem of
when a vector x∈ X is a double coboundary–ie is of the form x=(I− T)(I− S) y for some y∈ X …
when a vector x∈ X is a double coboundary–ie is of the form x=(I− T)(I− S) y for some y∈ X …
On limit theorems for fields of martingale differences
D Volný - Stochastic Processes and their Applications, 2019 - Elsevier
We prove a central limit theorem for stationary multiple (random) fields of martingale
differences f∘ T i ̲, i ̲∈ Z d, where T i ̲ is a Z d action. In most cases the multiple …
differences f∘ T i ̲, i ̲∈ Z d, where T i ̲ is a Z d action. In most cases the multiple …
Martingale-coboundary decomposition for stationary random fields
D Volny - arXiv preprint arXiv:1706.07978, 2017 - arxiv.org
We prove a martingale-coboundary representation for random fields with a completely
commuting filtration. For random variables in L2 we present a necessary and sufficient …
commuting filtration. For random variables in L2 we present a necessary and sufficient …
On the Quenched Functional Central Limit Theorem for Stationary Random Fields under Projective Criteria
L Reding, N Zhang - arXiv preprint arXiv:2106.01672, 2021 - arxiv.org
In this work we study and establish some quenched functional central limit theorems (CLT)
for stationary random fields under a projective criteria. These results are functional …
for stationary random fields under a projective criteria. These results are functional …