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作者：Addario-Berry, Louigi; Ford, Kevin
作者单位：McGill University; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We determine, to within 0(1), the expected minimal position at level n in certain branching random walks. The walks under consideration have displacement vector (nu 1, nu 2, ... ), where each vi is the sum of j independent Exponential(1) random variables and the different vi need not be independent. In particular, our analysis applies to the Poisson-Dirichlet branching random walk and to the Poisson-weighted infinite tree. As a corollary, we also determine the expected height of a random recur...
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作者：Ahdida, Abdelkoddousse; Alfonsi, Aurelien
作者单位：Universite Gustave-Eiffel; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：This work deals with the simulation of Wishart processes and affine diffusions on positive semidefinite matrices. To do so, we focus on the splitting of the infinitesimal generator in order to use composition techniques as did Ninomiya and Victoir [Appl. Math. Finance 15 (2008) 107-121] or Alfonsi [Math. Comp. 79 (2010) 209-237]. Doing so, we have found a remarkable splitting for Wishart processes that enables us to sample exactly Wishart distributions without any restriction on the parameters...
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作者：Bouchard, Bruno; Taflin, Erik
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Universite PSL; Universite Paris-Dauphine; CY Cergy Paris Universite; Ecole Internationale des Sciences du Traitement de linformation
摘要：Motivated by applications to bond markets, we propose a multivariate framework for discrete time financial markets with proportional transaction costs and a countable infinite number of tradable assets. We show that the no-arbitrage of second kind property (NA2 in short), recently introduced by Rasonyi for finite-dimensional markets, allows us to provide a closure property for the set of attainable claims in a very natural way, under a suitable efficient friction condition. We also extend to t...
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作者：Bayraktar, Erhan; Huang, Yu-Jui
作者单位：University of Michigan System; University of Michigan
摘要：This paper resolves a question proposed in Kardaras and Robertson [Ann. Appl. Probab. 22 (2012) 1576-1610]: how to invest in a robust growth-optimal way in a market where precise knowledge of the covariance structure of the underlying assets is unavailable. Among an appropriate class of admissible covariance structures, we characterize the optimal trading strategy in terms of a generalized version of the principal eigenvalue of a fully nonlinear elliptic operator and its associated eigenfuncti...
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作者：Bertini, Lorenzo; Faggionato, Alessandra; Gabrielli, Davide
作者单位：Sapienza University Rome; University of L'Aquila
摘要：We consider a lattice gas on the discrete d-dimensional torus (Z/NZ)(d) with a generic translation invariant, finite range interaction satisfying a uniform strong mixing condition. The lattice gas performs a Kawasaki dynamics in the presence of a weak external field E/N. We show that, under diffusive rescaling, the hydrodynamic behavior of the lattice gas is described by a nonlinear driven diffusion equation. We then prove the associated dynamical large deviation principle. Under suitable assu...
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作者：Pekoez, Erol A.; Roellin, Adrian; Ross, Nathan
作者单位：Boston University; National University of Singapore; University of California System; University of California Berkeley
摘要：We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed points of certain distributional transformations which allows us to obtain rates of convergence using a new variation of Stein's method. Despite the large literature on these models, there is surprisingly little known about the limiting distributions so we al...
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作者：Lindberg, Carl; Rootzen, Holger
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：This paper proves joint convergence of the approximation error for several stochastic integrals with respect to local Brownian semimartingales, for nonequidistant and random grids. The conditions needed for convergence are that the Lebesgue integrals of the integrands tend uniformly to zero and that the squared variation and covariation processes converge. The paper also provides tools which simplify checking these conditions and which extend the range for the results. These results are used t...
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作者：Acciaio, B.; Beiglboeck, M.; Penkner, F.; Schachermayer, W.; Temme, J.
作者单位：University of Vienna; University of Perugia
摘要：We present a unified approach to Doob's L-p maximal inequalities for 1 <= p < infinity. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a natural interpretation in terms of robust hedging. Moreover, our deterministic inequalities lead to new versions of Doob's maximal inequalities. These are best possible in the sense that equality is attained by properly chosen martingales.
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作者：Bertoin, Jean; Miermont, Gregory
作者单位：University of Zurich; Universite Paris Saclay
摘要：Consider the edge-deletion process in which the edges of some finite tree T are removed one after the other in the uniform random order. Roughly speaking, the cut-tree then describes the genealogy of connected components appearing in this edge-deletion process. Our main result shows that after a proper rescaling, the cut-tree of a critical Galton Watson tree with finite variance and conditioned to have size n, converges as n -> infinity to a Brownian continuum random tree (CRT) in the weak sen...
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作者：Galves, A.; Garcia, N. L.; Loecherbach, E.; Orlandi, E.
作者单位：Universidade Estadual de Campinas; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); CY Cergy Paris Universite; Roma Tre University
摘要：We consider a particle system on Z(d) with real state space and interactions of infinite range. Assuming that the rate of change is continuous we obtain a Kalikow-type decomposition of the infinite range change rates as a mixture of finite range change rates. Furthermore, if a high noise condition holds, as an application of this decomposition, we design a feasible perfect simulation algorithm to sample from the stationary process. Finally, the perfect simulation scheme allows us to forge an a...
