Central limit theorems for martingales-II: convergence in the weak dual topology [PDF]
Stochastic Analysis and Applications, 2023 . A convergence theorem for martingales with càdlàg trajectories (right continuous with left limits everywhere) is obtained in the sense of the weak dual topology on Hilbert space, under conditions that are much weaker than those required for any of the ...
B. Rémillard, J. Vaillancourt
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Central limit theorems for general transportation costs [PDF]
Annales De L Institut Henri Poincare-probabilites Et Statistiques, 2021 We consider the problem of optimal transportation with general cost between a empirical measure and a general target probability on R d , with d $\ge$ 1.
E. Barrio +2 more
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Stability of weak disorder phase for directed polymer with applications to limit theorems [PDF]
Latin American Journal of Probability and Mathematical Statistics, 2021 We study the directed polymer model in a bounded environment with bond disorder and show that, in the interior of the weak disorder phase, weak disorder continues to hold upon perturbation by a small bias. Using this stability result, we give a new proof
S. Junk
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Central Limit Theorem for Euclidean Minimal Spanning Acycles [PDF]
Journal of Topology and Analysis (JTA), 2022 We investigate asymptotics for the minimal spanning acycles of the (Alpha)-Delaunay complex on a stationary Poisson process on $\mathbb{R}^d, d \geq 2$.
P. Skraba, D. Yogeshwaran
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Random connection models in the thermodynamic regime: central limit theorems for add-one cost stabilizing functionals [PDF]
Electronic Journal of Probability, 2020 The paper deals with a random connection model, a random graph whose vertices are given by a homogeneous Poisson point process on $\R^d$, and edges are independently drawn with probability depending on the locations of the two end points.
Van Hao Can, Khanh Duy Trinh
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Well Posedness and Limit Theorems for a Class of Stochastic Dyadic Models [PDF]
SIAM Journal on Mathematical Analysis, 2022 We consider stochastic inviscid dyadic models with energy-preserving noise. It is shown that the models admit weak solutions which are unique in law. Under a certain scaling limit of the noise, the stochastic models converge weakly to a deterministic ...
Dejun Luo, Danli Wang
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Functional central limit theorems for rough volatility [PDF]
Finance and Stochastics, 2017 The non-Markovian nature of rough volatility makes Monte Carlo methods challenging, and it is in fact a major challenge to develop fast and accurate simulation algorithms.
Blanka Horvath +3 more
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A functional central limit theorem for branching random walks, almost sure weak convergence, and applications to random trees [PDF]
, 2014 Let $W_{\infty}(\beta)$ be the limit of the Biggins martingale $W_n(\beta)$ associated to a supercritical branching random walk with mean number of offspring $m$. We prove a functional central limit theorem stating that as $n\to\infty$ the process $$ D_n(
Rudolf Grubel, Z. Kabluchko
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Central limit theorems and suppression of anomalous diffusion for systems with symmetry [PDF]
, 2014 We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle/functional central limit theorem) to hold for observables of compact group extensions of nonuniformly expanding maps.
G. Gottwald, I. Melbourne
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Probabilistic limit theorems via the operator perturbation method, under optimal moment assumptions
Annales De L Institut Henri Poincare-probabilites Et Statistiques. The Nagaev-Guivarc’h operator perturbation method is well known to provide various probabilistic limit theorems for Markov random walks. A natural conjecture is that this method should provide these limit theorems under the same moment assumptions as ...
Françoise Pène
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