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作者：BERMAN, SM
摘要：Let X(t), t greater-than-or-equal-to 0, be a vector Gaussian process in R(m) whose components are i.i.d. copies of a real Gaussian process X(t) with stationary increments. Under specified conditions on the spectral distribution function used in the representation of the incremental variance function, it is shown that the self-intersection local time of multiplicity r of the vector process is jointly continuous. The dimension of the self-intersection set is estimated from above and below. The m...
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作者：FERRARI, PA; KIPNIS, C; SAADA, E
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Universite de Rouen Normandie
摘要：The one-dimensional nearest neighbor asymmetric simple exclusion process has been used as a microscopic approximation for the Burgers equation. This equation has travelling wave solutions. In this paper we show that those solutions have a microscopic structure. More precisely, we consider the simple exclusion process with rate p (respectively, q = 1 - p) for jumps to the right (left), 1/2 < p less-than-or-equal-to 1, and we prove the following results: There exists a measure mu on the space of...
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作者：FUNAKI, T; HANDA, K; UCHIYAMA, K
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology
摘要：Hydrodynamic behavior of one-dimensional homogeneous exclusion processes with speed change on periodic lattices Z/NZ, N = 1,2,3,..., is studied. For every reversible exclusion process with nearest neighbor jumps and local interactions of gradient type it is shown that under diffusion-type scaling in space and time the empirical density fields of the processes converge to a weak solution of a nonlinear diffusion equation as N goes to infinity. Two classes of examples of exclusion processes as s...
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作者：WANG, YH
摘要：In 1971, Simons and Johnson showed that the classical theorem of binomial to Poisson convergence is actually stronger than in the usual sense. Their result was proved valid also for the distributions of sums of independent, but not necessarily identically distributed, Bernoulli random variables by Chen in 1974. Here we show that their result is indeed true for a much larger class of random variables. The limiting distribution is generalized to a compound Poisson distribution.
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作者：MIKAMI, T
作者单位：Brown University
摘要：We consider the jump-type Markov processes which are small random perturbations of dynamical systems and their empirical processes. We prove large deviations theorems for empirical measures which are marginal measures of empirical processes at the exit time of Markov processes from a bounded domain in a d-dimensional Euclidean space R(d).
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作者：FREIDLIN, M
摘要：We consider single equations and systems of reaction-diffusion equations depending on small parameter. These equations are generalizations of the Kolmogorov-Petrovskii-Piskunov equation. Using the large deviation princple, we describe the asymptotic behavior of solutions.
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作者：ROSEN, J; YOR, M
作者单位：Sorbonne Universite
摘要：We develop explicit stochastic integral representations for the renormalized triple intersection local time of planar Brownian motion. Our representations involve a new type of double stochastic integral, the bilateral stochastic integral, which is developed in detail.
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作者：CARLEN, E; KREE, P
作者单位：Sorbonne Universite
摘要：For a continuous martingale M, let denote the increasing process. Let I0, I1,... denote the iterated stochastic integrals of M. We prove the inequalities of Burkholder-Davis-Gundy type, [GRAPHICS] where ln A(p,n) approximately ln B(p,n) approximately -(n/2)ln n as n --> infinity. Our proof requires the sharp constant b(p) in Burkholder-Davis-Gundy inequalities parallel-to M parallel-to p less-than-or-equal-to b(p) parallel-to 1/2 parallel-to p. In the Appendix we prove sup(p) greater-than-or-e...
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作者：MAULDIN, RD; VONWEIZSACKER, H
作者单位：University of Kaiserslautern
摘要：It is shown that a perturbed Bernoulli probability transition kernel yields an explicit example of an orthogonality preserving kernel which is not completely orthogonal. In statistical language, such a kernel defines models P(theta), theta-epsilon [0, 1], in which there is no estimate that estimates theta perfectly for all theta, but there is, for any given prior distribution on theta and hypothesis H0 subset-of [0, 1], a perfect test for H0 against its complement [0, 1] / H0. It is also demon...
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作者：LEE, TY
摘要：A critical branching Brownian motion in R(d) is studied where the initial state is either a single particle or a homogeneous field with finite or infinite density. Conditioned on survival in a bounded subset B of R(d) at a large time t, some normalized limits of the number of particles in a bounded subset A are obtained. When the initial state is a single particle, the normalization factor is a power of t in low dimensions, a power of log t in the critical dimension and a constant in high dime...
