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作者：Doeringa, Leif; Trottnerb, Lukas
作者单位：University of Mannheim
摘要：We prove precise stability results for overshoots of Markov additive processes (MAPs) with finite modulating space. Our approach is based on the Markovian nature of overshoots of MAPs whose mixing and ergodic proper-ties are investigated in terms of the characteristics of the MAP. On our way we extend fluctuation theory of MAPs, contributing among others to the understanding of the Wiener-Hopf factorization for MAPs by generalizing Vigon's equations amicales inverses known for Levy processes. ...
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作者：Buckdahn, Rainer; Li, Juan; Ma, Jin
作者单位：Universite de Bretagne Occidentale; Shandong University; Shandong University; University of Southern California
摘要：In this paper we consider a class of conditional McKean Vlasov SDES (CMVSDE for short). Such an SDE can be considered as an extended version of McKean-Vlasov SDEs with common noises, as well as the general version of the so-called conditional mean-field SDEs (CMFSDE) studied previously by the authors (Ann. Appl. Probab. 27 (2017) 3201-3245; SIAM J. Control Optim. 56 (2018) 1154-1180), but with some fundamental differences. In particular, due to the lack of compactness of the iterated condition...
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作者：Nguyen, Nhu; Yin, George
作者单位：University of Rhode Island; University of Connecticut
摘要：This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analy-sis, nonsmooth analysis, and stochastic differential inclusions. Under broad conditions, it is shown that a suitably scaled sequence of the iterates has a differential inclusion limit. In addition, it is shown for the first time that a centered and scaled sequence of the...
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作者：Wang, Feng-Yu
作者单位：Tianjin University
摘要：The convergence rate in Wasserstein distance is estimated for the em-pirical measures of symmetric semilinear SPDEs. Unlike in the finite -dimensional case that the convergence is of algebraic order in time, in the present situation the convergence is of log order with a power given by eigen-values of the underlying linear operator.
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作者：Puhalskii, Anatolii A.; Reed, Josh E.
作者单位：Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; New York University
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作者：Barbour, A. D.; Ross, Nathan; Zheng, Guangqu
作者单位：University of Zurich; University of Melbourne; University of Liverpool
摘要：We develop a general approach to Stein's method for approximating a random process in the path space D([0, T] -> Rd) by a real continuous Gaussian process. We then use the approach in the context of processes that have a representation as integrals with respect to an underlying point process, de-riving a general quantitative Gaussian approximation. The error bound is ex-pressed in terms of couplings of the original process to processes generated from the reduced Palm measures associated with t...
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作者：Kortchemski, Igor; Marzouk, Cyril
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We first establish new local limit estimates for the probability that a non -decreasing integer-valued random walk lies at time n at an arbitrary value, encompassing in particular large deviation regimes on the boundary of the Cramer zone. This enables us to derive scaling limits of such random walks conditioned by their terminal value at time n in various regimes. We believe both to be of independent interest. We then apply these results to obtain in-variance principles for the Lukasiewicz pa...
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作者：Leme, Renato Paes; Schneider, Jon
作者单位：Alphabet Inc.; Google Incorporated
摘要：We consider the problem of computing with many coins of unknown bias. We are given access to samples of n coins with unknown biases p1, . . . , pn and are asked to sample from a coin with bias f (p1, ... , pn) for a given function f : [0, 1]n -> [0, 1]. We give a complete characterization of the functions f for which this is possible. As a consequence, we show how to extend various combinatorial sampling procedures (most notably, the classic Sampford sampling for k-subsets) to the boundary of ...
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作者：Zhang, Deng
作者单位：Shanghai Jiao Tong University
摘要：We study the stochastic nonlinear Schrodinger equations with linear multiplicative noise, particularly in the defocusing mass-critical and energy -critical cases. For general initial data, we prove the global well-posedness of solutions in both mass-critical and energy-critical cases. We also prove the rescaled scattering behavior of global solutions in the spaces L-2, H-1 as well as the pseudo-conformal space for dimensions d >= 3 in the case of finite global quadratic variation of noise. Fur...
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作者：Charlier, Christophe; Moreillon, Philippe
作者单位：Royal Institute of Technology
摘要：The Pearcey process is a universal point process in random matrix theory. In this paper, we study the generating function of the Pearcey process on any number m of intervals. We derive an integral representation for it in terms of a Hamiltonian that is related to a system of 6m + 2 coupled nonlinear equations. We also obtain asymptotics for the generating function as the size of the intervals get large, up to and including the constant term. This work generalizes some results of Dai, Xu, and Z...
