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作者：Klump, Alexander; Savov, Mladen
作者单位：Bulgarian Academy of Sciences; University of Sofia
摘要：For areal-valued stochastic process (X-t)(t>0) we establish conditions under which the inverse first-passage time problem has a solution for any random variable xi> 0. For Markov processes we give additional conditions under which the solutions are unique and solutions corresponding to ordered initial states fulfill a comparison principle. As examples we show that these conditions include L & eacute;vy processes with infinite activity or unbounded variation and diffusions on an interval with a...
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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.
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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.
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作者：Aldous, David; Pittel, Boris
作者单位：University of California System; University of California Berkeley; University System of Ohio; Ohio State University
摘要：In the critical beta-splitting model of a random n-leaf binary tree, leaf- sets are recursively split into subsets, and a set of m leaves is split into subsets containing i and m - i leaves with probabilities proportional to 1/i(m - i). We study the continuous-time model in which the holding time before that split is exponential with rate hm-1, the harmonic number. We (sharply) evaluate the first two moments of the time-height Dn and of the edge-height Ln of a uniform random leaf (i.e., the le...
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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...
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作者：Cardaliaguet, Pierre; Seeger, Benjamin; Souganidis, Panagiotis
作者单位：Universite PSL; Universite Paris-Dauphine; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of Chicago
摘要：We study the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic and common noise. The unique feature of the problem is that the idiosyncratic noise coefficient may be degenerate, so that the system does not admit smooth solutions in general. We develop a new notion of weak solutions for backward stochastic Hamilton-Jacobi-Bellman equations, and use this to build probabilisticall...
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作者：Bou-rabee, Nawaf; Marsden, MILO.
作者单位：Rutgers University System; Rutgers University Camden; Rutgers University New Brunswick; Stanford University
摘要：A randomized time integrator is suggested for unadjusted Hamiltonian Monte Carlo (uHMC) which involves a very minor modification to the usual Verlet time integrator, and hence, is easy to implement. For target distributions of the form mu(dx) proportional to e-U(x) dx where U : Rd -> R >= 0 is K-strongly convex but only L-gradient Lipschitz, and initial distributions epsilon with finite second moment, coupling proofs reveal that an epsilon-accurate approximation of the target distribution in L...
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作者：Shen, Xiao
作者单位：Utah System of Higher Education; University of Utah
摘要：The study of Kadar-Parsi-Zhang (KPZ) universality class has been a subject of great interest among mathematicians and physicists over the past three decades. A notably successful approach for analyzing KPZ models is the coupling method, which hinges on understanding random growth from stationary initial conditions defined by Busemann functions. To advance in this direction, we investigate the independence property of the Busemann function across multiple directions in various exactly solvable ...
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作者：Leon, Jorge a.; Liu, Yanghui; Tindel, Samy
作者单位：CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional; City University of New York (CUNY) System; Baruch College (CUNY); Purdue University System; Purdue University
摘要：We prove that the Euler scheme for stochastic differential equations driven by fractional Brownian motions (fBm) with Hurst parameter H > 1/3 and its Malliavin derivatives are integrable uniformly in step size n. Then we use the integrability results to derive the weak convergence rate n1-4H+epsilon for the Euler scheme. The proof for integrability is based on an application of the argument of (Ann. Probab. 41 (2013) 3026-3050) to a quadratic functional of the fBm. The proof of weak convergenc...
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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 ...
