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作者：Hu, Yaozhong; Nualart, David; Song, Xiaoming
作者单位：University of Kansas
摘要：In this paper we study backward stochastic differential equations with general terminal value and general random generator. In particular, we do not require the terminal value be given by a forward diffusion equation. The randomness of the generator does not need to be from a forward equation, either. Motivated from applications to numerical simulations, first we obtain the L(p)-Holder continuity of the solution. Then we construct several numerical approximation schemes for backward stochastic...
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作者：Douc, Randal; Garivier, Aurelien; Moulines, Eric; Olsson, Jimmy
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Lund University
摘要：Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a foundation of particle-based approximation of such distributions and to analyze, in a common unifying framework, different schemes producing such approximations. In this setting, general convergence results, including exponential deviation inequalities and cen...
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作者：Fernholz, Daniel; Karatzas, Ioannis
摘要：In an equity market model with Knightian uncertainty regarding the relative risk and covariance structure of its assets, we characterize in several ways the highest return relative to the market that can be achieved using nonanticipative investment rules over a given time horizon, and under any admissible configuration of model parameters that might materialize. One characterization is in terms of the smallest positive supersolution to a fully nonlinear parabolic partial differential equation ...
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作者：Cerf, Raphael; Theret, Marie
作者单位：Universite Paris Saclay; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider the standard first passage percolation model in the rescaled graph Z(d)/n for d >= 2 and a domain Omega of boundary Gamma in R-d. Let Gamma(1) and Gamma(2) be two disjoint open subsets of Gamma representing the parts of Gamma through which some water can enter and escape from Omega. We investigate the asymptotic behavior of the flow phi(n) through a discrete version Omega(n) of Omega between the corresponding discrete sets Gamma(1)(n) and Gamma(2)(n). We prove that under some condi...
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作者：Kuznetsov, A.; Kyprianou, A. E.; Pardo, J. C.; van Schaik, K.
作者单位：York University - Canada; University of Bath; CIMAT - Centro de Investigacion en Matematicas
摘要：We develop a completely new and straightforward method for simulating the joint law of the position and running maximum at a fixed time of a general Levy process with a view to application in insurance and financial mathematics. Although different, our method takes lessons from Carr's so-called Canadization technique as well as Doney's method of stochastic bounds for Levy processes; see Carr [Rev. Fin. Studies 11 (1998) 597-626] and Doney [Ann. Probab. 32 (2004) 1545-1552]. We rely fundamental...
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作者：Barbato, David; Flandoli, Franco; Morandin, Francesco
作者单位：University of Padua; University of Pisa; University of Parma
摘要：A stochastic version of an inviscid dyadic model of turbulence, with multiplicative noise, is proved to exhibit energy dissipation in spite of the formal energy conservation. As a consequence, global regular solutions cannot exist. After some reductions, the main tool is the escape bahavior at infinity of a certain birth and death process.
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作者：Anderson, David F.; Ganguly, Arnab; Kurtz, Thomas G.
作者单位：University of Wisconsin System; University of Wisconsin Madison; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of different approximation methods and, specifically, Euler tau-leaping and midpoint tau-leaping. We perform our analysis under a scaling in which the size of the time discretization is inversely proportional to some (bounded) power of the norm of the state of th...
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作者：Bhamidi, Shankar; Bresler, Guy; Sly, Allan
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of California System; University of California Berkeley; Microsoft
摘要：A variety of random graph models has been developed in recent years to study a range of problems on networks, driven by the wide availability of data from many social, telecommunication, biochemical and other networks. A key model, extensively used in sociology literature, is the exponential random graph model. This model seeks to incorporate in random graphs the notion of reciprocity, that is, the larger than expected number of triangles and other small subgraphs. Sampling from these distribu...
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作者：Oreshkin, Boris N.; Coates, Mark J.
作者单位：McGill University
摘要：This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling the particles or by generating a parametric approximation. For such algorithms, we derive time-uniform bounds on the weak-sense L-p error and present associated exponential inequalities. We motivate the theoretical analysis by considering the leader node pa...
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作者：Burdzy, Krzysztof; Chen, Zhen-Qing; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We consider a family of hard core objects moving as independent Brownian motions confined to a vessel by reflection. These are subject to gravitational forces modeled by drifts. The stationary distribution for the process has many interesting implications, including an illustration of the Archimedes' principle. The analysis rests on constructing reflecting Brownian motion with drift in a general open connected domain and studying its stationary distribution. In dimension two we utilize known r...
