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作者：Liu, Song-hao; Zhang, Zhuo-song
作者单位：Southern University of Science & Technology
摘要：We establish Cramer-type moderate deviation theorems for the sums of locally dependent random variables and combinatorial central limit theorems. Optimal error bounds and convergence ranges are obtained under some mild exponential moment conditions. Our main results are more general or sharper than the results in the literature. The main results follow from a more gen-eral Cramer-type moderate deviation theorem for dependent random variables without any boundedness assumptions, which is of ind...
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作者：Alfonsi, Aurelien; Bally, Vlad
作者单位：Inria; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：We are concerned with a mixture of Boltzmann and McKean-Vlasov-type equations, this means (in probabilistic terms) equations with coefficients depending on the law of the solution itself, and driven by a Poisson point measure with the intensity depending also on the law of the solution. Both the analytical Boltzmann equation and the probabilistic interpretation ini-tiated by Tanaka (Z. Wahrsch. Verw. Gebiete 46 (1978/79) 67-105; J. Fac. Sci., Univ. Tokyo, Sect. IA, Math. 34 (1987) 351-369) hav...
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作者：Bayraktar, Erhan; Deng, Shuoqing; Norgilas, Dominykas
作者单位：University of Michigan System; University of Michigan; Hong Kong University of Science & Technology
摘要：The increasing supermartingale coupling, introduced by Nutz and Stebegg (Ann. Probab. 46 (2018) 3351-3398) is an extreme point of the set of supermartingale couplings between two real probability measures in convex-decreasing order. In the present paper we provide an explicit construction of a triple of functions, on the graph of which the increasing super -martingale coupling concentrates. In particular, we show that the increasing supermartingale coupling can be identified with the left-curt...
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作者：Isohatala, Jukka; Haskell, William B.
作者单位：National University of Singapore; Purdue University System; Purdue University
摘要：We present a new, tractable method for solving risk-aware problems over finite and infinite, discounted time-horizons where the dynamics of the con-trolled process are described using the martingale method. Supposing gen-eral Polish state and action spaces, and using the martingale characteriza-tion, we state a risk-aware dynamic optimal control problem of minimizing risk of costs described by a generic risk function. From this, we construct an alternative formulation of the optimization probl...
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作者：Leimkuhler, Benedict; Sharma, Akash; V. Tretyakov, Michael
作者单位：University of Edinburgh; University of Edinburgh; Heriot Watt University; University of Nottingham
摘要：A simple-to-implement weak-sense numerical method to approximate reflected stochastic differential equations (RSDEs) is proposed and analysed. It is proved that the method has the first order of weak convergence. Together with the Monte Carlo technique, it can be used to numerically solve linear parabolic and elliptic PDEs with Robin boundary condition. One of the key results of this paper is the use of the proposed method for computing ergodic limits, that is, expectations with respect to the...
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作者：Cai, Xing shi; Caputo, Pietro; Perarnau, Guillem; Quattropani, Matteo
作者单位：Duke Kunshan University; Roma Tre University; Centre de Recerca Matematica (CRM); Universitat Politecnica de Catalunya; Sapienza University Rome
摘要：We consider the extremal values of the stationary distribution of sparse directed random graphs with given degree sequences and their relation to the extremal values of the in-degree sequence. The graphs are generated by the directed configuration model. Under the assumption of bounded (2 + eta)moments on the in-degrees and of bounded out-degrees, we obtain tight comparisons between the maximum value of the stationary distribution and the maximum in-degree. Under the further assumption that th...
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作者：Conforti, Giovanni
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We investigate the long time behavior of weakly dissipative semilinear Hamilton-Jacobi-Bellman (HJB) equations and the turnpike property for the corresponding stochastic control problems. To this aim, we develop a proba-bilistic approach based on a variant of coupling by reflection adapted to the study of controlled diffusion processes. We prove existence and uniqueness of solutions for the ergodic Hamilton-Jacobi-Bellman equation and different kind of quantitative exponential convergence resu...
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作者：Fehrman, Benjamin
作者单位：University of Oxford
摘要：We provide a proof of stochastic homogenization for random environ-ments with a mean zero, divergence-free drift. We prove that the environ-ment homogenizes weakly in H1 if the drift admits a stationary L2-integrable stream matrix, and we prove that the two-scale expansion converges strongly in H1 if the drift admits a stationary Ld & PROVES;(2+& delta; )-integrable stream matrix. Ad-ditionally, under this stronger integrability assumption, we show that the en-vironment almost surely satisfies...
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作者：Clement, Emmanuelle
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：In this paper, we get some convergence rates in total variation distance in approximating discretized paths of Levy driven stochastic differential equa-tions, assuming that the driving process is locally stable. The particular case of the Euler approximation is studied. Our results are based on sharp local estimates in Hellinger distance obtained using Malliavin calculus for jump processes.
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作者：Mueller-Gronbach, Thomas; Yaroslavtseva, Larisa
作者单位：University of Passau
摘要：In the past decade, an intensive study of strong approximation of stochas-tic differential equations (SDEs) with a drift coefficient that has discontinu-ities in space has begun. In the majority of these results it is assumed that the drift coefficient satisfies piecewise regularity conditions and that the diffusion coefficient is globally Lipschitz continuous and nondegenerate at the discon-tinuities of the drift coefficient. Under this type of assumptions the best L-p-error rate obtained so ...
