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作者：Hao, Tao; Hu, Ying; Tang, Shanjian; Wen, Jiaqiang
作者单位：Shandong University of Finance & Economics; Centre National de la Recherche Scientifique (CNRS); Universite de Rennes; Fudan University; Fudan University; Southern University of Science & Technology; Southern University of Science & Technology
摘要：In this paper, we study general mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. First, using some new ideas, we prove the existence and uniqueness of local and global solutions for a one-dimensional mean-field BSDE when the generator g(t,Y, Z,PY, PZ) has quadratic growth in Z and the terminal value is bounded. Second, we derive a comparison theorem for general mean-field BSDEs by applying the Girsanov transform. Third, within this framework, we u...
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作者：Lu, Huaxiang; Zhu, Xiangchan
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：In this paper we are concerned with the 2D incompressible Navier- Stokes equations driven by space-time white noise. We establish existence of solutions u for every divergence free initial condition u(0) is an element of L-p boolean OR C-1+delta, p is an element of (1, 2), delta > 0. More precisely, there exist infinitely many solutions such that u - z is an element of C([0, infinity); L-p) fl L-loc(2)([0, infinity); H-zeta) fl L-loc(1)([0, oo); W-1/3.1) for some zeta E (0, 1), where z is the ...
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作者：Chong, Carsten H.; Todorov, Viktor
作者单位：Hong Kong University of Science & Technology; Northwestern University
摘要：We derive a nonparametric higher-order asymptotic expansion for smalltime changes of conditional characteristic functions of It & ocirc; semimartingale increments. The asymptotics setup is of joint type: both the length of the time interval of the increment of the underlying process and the time gap between evaluating the conditional characteristic function are shrinking. The spot semimartingale characteristics of the underlying process as well as their spot semimartingale characteristics appe...
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作者：Hermon, Jonathan; Sarkovic, Andela; Sousi, Perla
作者单位：University of British Columbia; University of Cambridge
摘要：We consider a variant of the configuration model with an embedded community structure and study the mixing properties of a simple random walk on it. Every vertex has an internal degint >= 3 and an outgoing degout number of half-edges. Given a stochastic matrix Q, we pick a random perfect matching of the half-edges subject to the constraint that each vertex v has degint(v) neighbours inside its community and the proportion of outgoing half-edges from community i matched to a half-edge from comm...
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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：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：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：Zhang, Xuhui; Blanchet, Jose; Marzouk, Youssef; Nguyen, Viet Anh; Wang, Sven
作者单位：Stanford University; Massachusetts Institute of Technology (MIT); Chinese University of Hong Kong; Humboldt University of Berlin
摘要：We study a distributionally robust optimization formulation (i.e., a min-max game) for two representative problems in Bayesian nonparametric estimation: Gaussian process regression and, more generally, linear inverse problems. Our formulation seeks the best mean-squared error predictor in an infinite-dimensional space against an adversary who chooses the worst-case model in a Wasserstein ball around a nominal infinite-dimensional Bayesian model. The transport cost is chosen to control features...
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作者：Khudiakova, Ksenia A.; Maas, Jan; Pedrotti, Francesco
作者单位：Institute of Science & Technology - Austria
摘要：We prove upper bounds on the L infinity-Wasserstein distance from optimal transport between strongly log-concave probability densities and logLipschitz perturbations. In the simplest setting, such a bound amounts to a transport-information inequality involving the L infinity-Wasserstein metric and the relative L infinity-Fisher information. We show that this inequality can be sharpened significantly in situations where the involved densities are anisotropic. Our proof is based on probabilistic...
