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作者：Escauriaza, Luis; Schwarz, Daniel C.; Xing, Hao
作者单位：University of Basque Country; University of London; University College London; Boston University
摘要：Motivated by an equilibrium problem, we establish the existence of a solution for a family of Markovian backward stochastic differential equations with quadratic nonlinearity and discontinuity in Z. Using unique continuation and backward uniqueness, we show that the set of discontinuity has measure zero. In a continuous-time stochastic model of an endowment economy, we prove the existence of an incomplete Radner equilibrium with nondegenerate endogenous volatility.
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作者：Duerinckx, Mitia; Fischer, Julian; Gloria, Antoine
作者单位：Universite Libre de Bruxelles; Institute of Science & Technology - Austria; Sorbonne Universite; Universite Paris Cite
摘要：Consider a linear elliptic partial differential equation in divergence form with a random coefficient field. The solution-operator displays fluctuations around its expectation. The recently-developed pathwise theory of fluctuations in stochastic homogenization reduces the characterization of these fluctuations to those of the so-called standard homogenization commutator. In this contribution, we investigate the scaling limit of this key quantity: starting from a Gaussian-like coefficient field...
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作者：Lerouvillois, Vincent; Toninelli, Fabio
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Technische Universitat Wien
摘要：The Markov dynamics of interlaced particle arrays, introduced by A. Borodin and P. L. Ferrari in (Comm. Math. Phys. 325 (2014) 603-684), is a classical example of (2 + 1)-dimensional random growth model belonging to the so-called Anisotropic KPZ universality class. In (Comm. Pure Appl. Math. 72 (2018) 620-666), a hydrodynamic limit-the convergence of the height profile, after space/time rescaling, to the solution of a deterministic Hamilton-Jacobi PDE with nonconvex Hamiltonian-was proven when...
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作者：Gu, Chenlin
作者单位：Universite PSL; Ecole Normale Superieure (ENS)
摘要：We present an efficient algorithm to solve elliptic Dirichlet problems defined on the cluster of supercritical Z(d)-Bernoulli percolation, as a generalization of the iterative method proposed by S. Armstrong, A. Hannukainen, T. Kuusi and J.-C. Mourrat (ESAIM Math. Model. Numer. Anal. (2021) 55 37-55). We also explore the two-scale expansion on the infinite cluster of percolation, and use it to give a rigorous analysis of the algorithm.
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作者：Addario-Berry, Louigi; Devroye, Luc; Lugosi, Gabor; Velona, Vasiliki
作者单位：McGill University; McGill University; ICREA; Pompeu Fabra University; Universitat Politecnica de Catalunya
摘要：We study the broadcasting problem when the underlying tree is a random recursive tree. The root of the tree has a random bit value assigned. Every other vertex has the same bit value as its parent with probability 1 - q and the opposite value with probability q, where q is an element of [0, 1]. The broadcasting problem consists in estimating the value of the root bit upon observing the unlabeled tree, together with the bit value associated with every vertex. In a more difficult version of the ...
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作者：Hu, Ying; Shi, Xiaomin; Xu, Zuo Quan
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); Shandong University of Finance & Economics; Hong Kong Polytechnic University
摘要：This paper is concerned with a stochastic linear-quadratic optimal control problem with regime switching, random coefficients and cone control constraint. The randomness of the coefficients comes from two aspects: the Brownian motion and the Markov chain. Using Ito's lemma for Markov chain, we obtain the optimal state feedback control and optimal cost value explicitly via two new systems of extended stochastic Riccati equations (ES-REs). We prove the existence and uniqueness of the two ESREs u...
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作者：Arapostathis, Ari; Biswas, Anup
作者单位：University of Texas System; University of Texas Austin; Indian Institute of Science Education & Research (IISER) Pune
摘要：We consider a class of diffusions controlled through the drift and jump size, and driven by a jump Levy process and a nondegenerate Wiener pro-cess, and we study infinite horizon (ergodic) risk-sensitive control problems for this model. We start with the controlled Dirichlet eigenvalue problem in smooth bounded domains, which also allows us to generalize current results in the literature on exit rate control problems. Then we consider the infi-nite horizon average risk-sensitive minimization a...
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作者：Finn, Thomas; Stauffer, Alexandre
作者单位：University of Bath; Roma Tre University
摘要：We introduce a two-type first passage percolation competition model on infinite connected graphs as follows. Type 1 spreads through the edges of the graph at rate 1 from a single distinguished site, while all other sites are initially vacant. Once a site is occupied by type 1, it converts to type 2 at rate p > 0. Sites occupied by type 2 then spread at rate lambda > 0 through vacant sites and sites occupied by type 1, whereas type 1 can only spread through vacant sites. If the set of sites occ...
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作者：Berger, Noam; Procaccia, Eviatar B.; Turner, Amanda
作者单位：Technical University of Munich; Technion Israel Institute of Technology; University of Leeds
摘要：We construct and study a stationary version of the Hastings-Levitov(0) model. We prove that, unlike in the classical HL(0) model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL(0) is proposed as a potential candidate for a stationary off-lattice variant of diffusion limited aggregation (DLA). The stationary setting, together with a geometric interpretation of the harmonic measure, yields new geometric results such as stabilization, finitenes...
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作者：Bhamidi, Shankar; Budhiraja, Amarjit; Dupuis, Paul; Wu, Ruoyu
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University; Iowa State University
摘要：Large deviations for random graph models has been a topic of significant recent research activity. Much work in this area is focused on the class of dense random graph models (number of edges in the graph scale as n(2), where n is the number of vertices) where the theory of graphons has emerged as a principal tool in the study of large deviation properties. These tools do not give a good approach to large deviation problems for random graph models in the sparse regime. The aim of this paper is...
