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作者：Goldstein, Larry; Penrose, Mathew D.
作者单位：University of Southern California; University of Bath
摘要：We give error bounds which demonstrate optimal rates of convergence in the CLT for the total covered volume and the number of isolated shapes, for germ-grain models with fixed grain radius over a binomial point process of n points in a toroidal spatial region of volume n. The proof is based on Stein's method via size-biased couplings.
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作者：Dolinsky, Yan
作者单位：Hebrew University of Jerusalem
摘要：In this paper we consider Dynkin's games with payoffs which are functions of an underlying process. Assuming extended weak convergence of underlying processes {S-(n)}(n=0)(infinity) to a limit process S we prove convergence Dynkin's games values corresponding to {S(n)}(n=0)(infinity) to the Dynkin's game value corresponding to S. We use these results to approximate game options prices with path dependent payoffs in continuous time models by a sequence of game options prices in discrete time mo...
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作者：Jenkins, Paul A.; Song, Yun S.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Ewens sampling formula (ESF) is a one-parameter family of probability distributions with a number of intriguing combinatorial connections. This elegant closed-form formula first arose in biology as the stationary probability distribution of a sample configuration at one locus under the infinite-alleles model of mutation. Since its discovery in the early 1970s, the ESF has been used in various biological applications, and has sparked several interesting mathematical generalizations. In the popu...
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作者：Goldman, Andre
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We prove that the Palm measure of the Ginibre process is obtained by removing a Gaussian distributed point from the process and adding the origin. We obtain also precise formulas describing the law of the typical cell of Ginibre-Voronoi tessellation. We show that near the germs of the cells a more important part of the area is captured in the Ginibre-Voronoi tessellation than in the Poisson-Voronoi tessellation. Moment areas of corresponding subdomains of the cells are explicitly evaluated.
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作者：Saksman, Eero; Vihola, Matti
作者单位：University of Helsinki; University of Jyvaskyla
摘要：This paper describes sufficient conditions to ensure the correct ergodicity of the Adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen [Bernoulli 7 (2001) 223-242] for target distributions with a noncompact support. The conditions ensuring a strong law of large numbers require that the tails of the target density decay super-exponentially and have regular contours. The result is based on the ergodicity of an auxiliary process that is sequentially constrained to feasible adaptati...
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作者：Fontbona, J.
作者单位：Universidad de Chile; Universidad de Chile; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We develop a McKean-Vlasov interpretation of Navier-Stokes equations with external force field in the whole space, by associating with local mild L(p)-solutions of the 3d-vortex equation a generalized nonlinear diffusion with random space-time birth that probabilistically describes creation of rotation in the fluid due to nonconservativeness of the force. We establish a local well-posedness result for this process and a stochastic representation formula for the vorticity in terms of a vector-w...
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作者：Barlow, Martin T.; Zheng, Xinghua
作者单位：University of British Columbia; Hong Kong University of Science & Technology
摘要：We consider a random walk in an lid. Cauchy-tailed conductances environment. We obtain a quenched functional CLT for the suitably rescaled random walk, and, as a key step in the arguments, we improve the local limit theorem for p(n)(omega)2(t)(0, y) in [Ann. Probab. (2009). To appear], Theorem 5.14, to a result which gives uniform convergence for p(n)(omega)2(t) (x, y) for all x, y in a ball.
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作者：Mischaikow, Konstantin; Wanner, Thomas
作者单位：Rutgers University System; Rutgers University New Brunswick; George Mason University
摘要：Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications, these structures can be expressed as nodal domains of real-valued functions and are obtained only through experimental observation or numerical simulations. In both cases, the data on which the topological measurements are based are derived via some form of finite sampling or discretization. In this paper, we present a probabilistic approach to quantifying the...
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作者：Armendariz, Ines
摘要：We introduce a one-dimensional stochastic system where particles perform independent diffusions and interact through pairwise coagulation events, which occur at a nontrivial rate upon collision. Under appropriate conditions on the diffusion coefficients, the coagulation rates and the initial distribution of particles, we derive a spatially inhomogeneous version of the mass flow equation as the particle number tends to infinity. The mass flow equation is in one-to-one correspondence with Smoluc...
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作者：Evans, Steven N.; Sturmfels, Bernd; Uhler, Caroline
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We use methods from combinatorics and algebraic statistics to study analogues of birth-and-death processes that have as their state space a finite subset of the m-dimensional lattice and for which the in matrices that record the transition probabilities in each of the lattice directions commute pair-wise. One reason such processes are of interest is that the transition matrix is straightforward to diagonalize, and hence it is easy to compute n step transition probabilities. The set of commutin...
