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作者：Wuthrich, MV
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider d-dimensional Brownian motion in a truncated Poissonian potential conditioned to reach a remote location. If Brownian motion starts at the origin and ends in an hyperplane at distance L from the origin, the transverse fluctuation of the path is expected to be of order L-xi. We are interested in a lower bound for xi. We first show that xi greater than or equal to 1/2 in dimensions d greater than or equal to 2 and then we prove superdiffusive behavior for d = 2, resulting in xi great...
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作者：Ethier, SN; Kurtz, TG
作者单位：Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：Fleming-Viot processes are probability-measure-valued diffusion processes that can be used as stochastic models in population genetics. Here we use duality methods to prove ergodic theorems for Fleming-Viot processes, including those with recombination. Coupling methods are also used to establish ergodicity of Fleming-Viot processes, first without and then with selection. A special type of selection known as symmetric overdominance is treated by other methods.
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作者：Sturm, KT
作者单位：University of Bonn
摘要：We present a general method to construct m-symmetric diffusion processes (X-t,P-x) on any given locally compact metric space (X,d) equipped with a Radon measure m. These processes are associated with local regular Dirichlet forms which are obtained as Gamma-limits of approximating nonlocal Dirichlet forms. This general method works without any restrictions on (X, d, m) and yields processes which are well defined for quasi every starting point. The second main topic of this paper is to formulat...
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作者：Zerner, MPW
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Assign to the lattice sizes z is an element of Z(d) i.i.d. random 2d-dimensional vectors (omega(z, z + e))(/e/ = 1) whose entries take values in the open unit interval and add up to one. Given a realization w of this environment, let (X-n)(n greater than or equal to 0) be a Markov chain on hd which, when at z, moves one step to its neighbor z + e with transition probability omega(z, z + e). We derive a large deviation principle for X-n/n by means of a result similar to the shape theorem of fir...
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作者：de Acosta, A; Ney, P
作者单位：University System of Ohio; Case Western Reserve University; University of Wisconsin System; University of Wisconsin Madison
摘要：A universal large deviation lower bound is proved for sums of Banach space valued functions of an irreducible, general state space Markov chain. There are no restrictions on the functions (other than measurability).
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作者：Klenke, A
作者单位：University of Erlangen Nuremberg
摘要：We consider two spatial branching models on R-d: branching Brownian motion with a branching law in the domain of normal attraction of a (1 + beta) stable law, 0 < beta less than or equal to 1, and the corresponding high density limit measure valued diffusion. The longtime behavior of both models depends highly on beta and d. We show that for d less than or equal to 2/beta the only invariant measure is delta(0), the unit mass on the empty configuration. Furthermore, we give a precise condition ...
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作者：Peligrad, M
作者单位：University System of Ohio; University of Cincinnati
摘要：In this paper, we study the weak convergence to an appropriate Gaussian process of the empirical process of the block-based bootstrap estimator proposed by Kunsch for stationary sequences. The classes of processes investigated are weak dependent and associated sequences. We also prove that, differently from the independent situation, the bootstrapped estimator of the mean of certain dependent sequences satisfies the central limit theorem while the mean of the original sequence does not.
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作者：Comets, F; Menshikov, M; Popov, S
作者单位：Universite Paris Cite; Universidade de Sao Paulo
摘要：We study two typical examples of countable Markov chains in random environment using the Lyapunov functions method: random walk and random string in random environment. In each case we construct an explicit Lyapunov function. Investigating the behavior of this function, we get the classification for recurrence, transience, ergodicity. We obtain new results for random strings in random environment, though we simply review well-known results for random walks using our approach.
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作者：Gantert, N
作者单位：Technical University of Berlin
摘要：For an i.i.d. sequence of random variables with a semiexponential distribution, we give a functional form of the Erdos-Renyi law for partial sums. In contrast to the classical case, that is, the case where the random variables have exponential moments of all orders, the set of limit points is not a subset elf the continuous functions. This reflects the bigger influence of extreme values. The proof is based on a large deviation principle for the trajectories of the corresponding random walk. Th...
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作者：Jacod, J; Protter, P
作者单位：Sorbonne Universite; Purdue University System; Purdue University
摘要：We are interested in the rate of convergence of the Euler scheme approximation of the solution to a stochastic differential equation driven by a general (possibly discontinuous) semimartingale, and by the asymptotic behavior of the associated normalized error. It is well known that for Ito's equations the rate is 1/root n;we provide a necessary and sufficient condition for this rate to be 1 root n when the driving semimartingale is a continuous martingale, or a continuous semimartingale under ...
