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作者：Possamai, Dylan; Tan, Xiaolu; Zhou, Chao
作者单位：Universite PSL; Universite Paris-Dauphine; National University of Singapore
摘要：We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimization, over a set of possibly nondominated probability measures, of solutions of backward stochastic differential equations (BSDEs). Since BSDEs are nonlinear generalizations of the traditional (linear) expectations, this problem can be understood as stochastic control of a family of nonlinear expectations, or equivalently of nonlinear kernels. Our first mai...
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作者：Xing, Hao; Zitkovic, Gordan
作者单位：University of London; London School Economics & Political Science; University of Texas System; University of Texas Austin
摘要：We establish existence and uniqueness for a wide class of Markovian systems of backward stochastic differential equations (BSDE) with quadratic nonlinearities. This class is characterized by an abstract structural assumption on the generator, an a priori local-boundedness property, and a locally-Holder-continuous terminal condition. We present easily verifiable sufficient conditions for these assumptions and treat several applications, including stochastic equilibria in incomplete financial ma...
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作者：Bordenave, Charles; Caputo, Pietro; Chafai, Djalil; Tikhomirov, Konstantin
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Roma Tre University; Universite PSL; Universite Paris-Dauphine; Princeton University
摘要：Consider a square matrix with independent and identically distributed entries of zero mean and unit variance. It is well known that if the entries have a finite fourth moment, then, in high dimension, with high probability, the spectral radius is close to the square root of the dimension. We conjecture that this holds true under the sole assumption of zero mean and unit variance. In other words, that there are no outliers in the circular law. In this work, we establish the conjecture in the ca...
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作者：Dobler, Christian; Peccati, Giovanni
作者单位：University of Luxembourg
摘要：We prove a fourth moment bound without remainder for the normal approximation of random variables belonging to the Wiener chaos of a general Poisson random measure. Such a result-that has been elusive for several years-shows that the so-called 'fourth moment phenomenon', first discovered by Nualart and Peccati [Ann. Probab. 33 (2005) 177-193] in the context of Gaussian fields, also systematically emerges in a Poisson framework. Our main findings are based on Stein's method, Malliavin calculus ...
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作者：Cannizzaro, Giuseppe; Chouk, Khalil
作者单位：University of Warwick; Technical University of Berlin
摘要：We study the existence and uniqueness of solution for stochastic differential equations with distributional drift by giving a meaning to the Stroock-Varadhan martingale problem associated to such equations. The approach we exploit is the one of paracontrolled distributions introduced in (Forum Math. Pi 3 ( 2015) e6). As a result, we make sense of the three-dimensional polymer measure with white noise potential.
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作者：Marinelli, Carlo; Scarpa, Luca
作者单位：University of London; University College London
摘要：We prove global well-posedness for a class of dissipative semilinear stochastic evolution equations with singular drift and multiplicative Wiener noise. In particular, the nonlinear term in the drift is the superposition operator associated to a maximal monotone graph everywhere defined on the real line, on which neither continuity nor growth assumptions are imposed. The hypotheses on the diffusion coefficient are also very general, in the sense that the noise does not need to take values in s...
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作者：Shiraishi, Daisuke
作者单位：Kyoto University
摘要：Let M-n be the number of steps of the loop- erasure of a simple random walk on Z(3) run until its first exit from a ball of radius n. In the paper, we will show the existence of the growth exponent, that is, we show that there exists beta > 0 such that (n ->infinity)lim log E (M-n)/log n = beta.
