-
作者：Han, Xiyue; Schied, Alexander
作者单位：University of Waterloo
摘要：Motivated by pathwise stochastic calculus, we say that continuous real-valued function x admits the roughness exponent R if the pth variation of x converges to zero for p > 1/R and to infinity for p < 1/R. In our main result, we provide a mild condition on the Faber-Schauder coefficients of x under which the roughness exponent exists and is given as the limit of the classical Gladyshev estimates R-n(x). This result can be viewed as a strong consistency result for the Gladyshev estimators in an...
-
作者：Pammer, Gudmund; Robinson, Benjamin A.; Schachermayer, Walter
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Klagenfurt; University of Vienna
摘要：We present a multidimensional extension of Kellerer's theorem on the existence of mimicking Markov martingales for peacocks, a term derived from the French for stochastic processes increasing in convex order. For a continuous-time peacock in arbitrary dimension, after Gaussian regularization, we show that there exists a strongly Markovian mimicking martingale It & ocirc; diffusion. A novel compactness result for martingale diffusions is a key tool in our proof. Moreover, we provide counterexam...
-
作者：Budzinski, Thomas; Contat, Alice; Curien, Nicolas
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：We study the Karp-Sipser core of a random graph made of a configuration model with vertices of degree 1, 2 and 3. This core is obtained by recursively removing the leaves as well as their unique neighbors in the graph. We settle a conjecture of Bauer and Golinelli ( (Eur. Phys. J. B 24 (2001) 339-352) and prove that at criticality, the Karp-Sipser core has size approximate to Cst . .theta .theta- .theta-2 . n n3/5 where theta is the hitting time of the curve t -> 1 t t2 by a linear Brownian mo...
-
作者：Bertoin, Jean; Mallein, Bastien
作者单位：University of Zurich; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Reinforced Galton-Watson processes have been introduced in (Ran-dom Structures Algorithms 65 (2024) 387-410) as population models with nonoverlapping generations, such that reproduction events along genealogical lines can be repeated at random. We investigate here some of their sample path properties such as asymptotic growth rates and survival, for which the effects of reinforcement on the evolution appear quite strikingly.
-
作者：Journel, Lucas; Monmarche, Pierre
作者单位：University of Neuchatel; Universite Paris Cite; Sorbonne Universite
摘要：We study the long-time convergence of a Fleming-Viot process, in the case where the underlying process is a metastable diffusion killed when it reaches some level set. Through a coupling argument, we establish the longtime convergence of the Fleming-Viot process toward some stationary measure at an exponential rate independent of N, the size of the system, as well as uniform in time propagation of chaos estimates.
-
作者：Gaudio, Julia; Racz, Milkos Z.; Sridhar, Anirudh
作者单位：Northwestern University; Northwestern University; Northwestern University; Massachusetts Institute of Technology (MIT)
摘要：We propose a simple and efficient local algorithm for graph isomorphism which succeeds for a large class of sparse graphs. This algorithm produces a low-depth canonical labeling, which is a labeling of the vertices of the graph that identifies its isomorphism class using vertices' local neighborhoods. Prior work by Czajka and Pandurangan showed that in the Erdos-R & eacute;nyi model G(n, pn), the degree profile of a vertex (i.e., the sorted list of the degrees of its neighbors) gives a canonic...
-
作者：Han, Yi
作者单位：University of Cambridge
摘要：In this paper we explore the merit of relative entropy in proving weak well-posedness of McKean-Vlasov SDEs and SPDEs, extending the technique introduced in Lacker (Probab. Math. Phys. 4 (2023) 377-432). In the SDE setting, we prove weak existence and uniqueness when the interaction is path dependent and only assumed to have linear growth. Meanwhile, we recover and extend the current results when the interaction has Krylov's L-t(q)-L-x(p) type singularity for (d)/(p)+(2)/(q)<1, where d is the ...
-
作者：Villemonais, Denis; Watson, Alexander R.
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Institut Universitaire de France; University of London; University College London
摘要：In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the sizes of cells settles into an equilibrium asymptotic profile. In this work we introduce a new method to prove this asymptotic behaviour for the growth-fragmentation equation, and show that the convergence to the asymptotic profile occurs at exponential rate. We do this by identifying an associated sub-Markov process...
-
作者：Chen, Zaiwei; Maguluri, Siva Theja; Zubeldia, Martin
作者单位：Purdue University System; Purdue University; University System of Georgia; Georgia Institute of Technology; University of Minnesota System; University of Minnesota Twin Cities
摘要：In this paper, we establish maximal concentration bounds for the iterates generated by a stochastic approximation (SA) algorithm under a contractive operator with respect to some arbitrary norm (e.g., the pound infinity-norm). We consider two settings where the iterates are potentially unbounded: SA with bounded multiplicative noise and SA with sub-Gaussian additive noise. Our maximal concentration inequalities state that the convergence error has a sub-Gaussian tail in the additive noise sett...
-
作者：Gerolla, Luca; Hairer, Martin; Li, Xue-Mei
作者单位：Imperial College London; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We study the large-scale dynamics of the solution to a nonlinear stochastic heat equation (SHE) in dimensions d >= 3 with long-range dependence. This equation is driven by multiplicative Gaussian noise, which is white in time and coloured in space with nonintegrable spatial covariance that decays at the rate of |x|-kappa at infinity, where kappa E (2, d). Inspired by recent studies on SHE and KPZ equations driven by noise with compactly supported spatial correlation, we demonstrate that the co...
