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1.
We study the path behaviour of the anisotropic random walk on the two-dimensional lattice ?2. Strong approximation of its components with independent Wiener processes is proved. We also give some asymptotic results for the local time in the periodic case.  相似文献   

2.
Let μ be a probability measure on a locally compact second countable groupG defining a recurrent (but not necessarily Harris) random walk. Denote byG the space of paths and byB (a)the asymptotic σ-algebra. Let the starting measure be equivalent to the Haar measure and writeQ for the corresponding Markov measure onG . We prove thatL (G, B(a), Q) is in a canonical way isomorphic toL (G/N) whereN is the smallest closed normal subgroup ofG such that μ(zN)=1 for somez∈G. The groupG/N is either a finite cyclic group with generatorzN or a compact abelian group having the cyclic group as a dense subgroup. As a corollary we obtain that the set of all φ∈L 1(G) such that coincides with the kernel of the canonical mapping ofL 1(G)ontoL 1(G/N). In particular, when μ is aperiodic, i.e.,G=N, then the random walk is mixing: for every φ∈L 1(G) with ∝ φ=0.  相似文献   

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A nonhomogeneous random walk on the grid ℤ1 with transition probabilities that differ from those of a certain homogeneous random walk only at a finite number of points is considered. Trajectories of such a walk are proved to converge to trajectories of a certain generalized diffusion process on the line. This result is a generalization of the well-known invariance principle for the sums of independent random variables and Brownian motion. Translated fromMatematicheskie Zametki, Vol. 66, No. 3, pp. 459–472, September, 1999.  相似文献   

5.
In the present paper, we study the σ-algebra of pasts Ξ = {ξ n } n of a random walk T over the orbits of a Bernoulli action of the group Zd. We calculate the proper scaling and the scaling entropy of this sequence of partitions. We show that the proper scaling entropy of the σ-algebra of pasts is equal to . Bibliography: 4 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 325, 2005, pp. 103–112.  相似文献   

6.
We prove that loop-erased random walks on the finite pre-Sierpiński gaskets can be extended to a loop-erased random walk on the infinite pre-Sierpiński gasket by using the ‘erasing-larger-loops-first’ method, and obtain the asymptotic behavior of the walk as the number of steps increases, in particular, the displacement exponent and a law of the iterated logarithm.  相似文献   

7.
Two alternate arguments in the framework of intrinsic metrics and measures respectively of part of the proof of a famous theorem due to Qi-Keng Lu on Bergman metric with constant negative holomorphic sectional curvature are presented.A relationship between the Lu constant and the holo- morphic sectional curvature of the Bergman metric is given.Some recent progress of the Yau's porblem on the characterization of domain of holomorphy on which the Bergman metric is K(?)hler-Einstein is described.  相似文献   

8.
We consider the Potts model on the set in the field Q p of p-adic numbers. The range of the spin variables (n), , in this model is . We show that there are some values q=q(p) for which phase transitions occur.  相似文献   

9.
This paper presents a novel technique for deriving asymptotic expressions for the occurrence of rare events for a random walk in the quarter plane. In particular, we study a tandem queue with Poisson arrivals, exponential service times and coupled processors. The service rate for one queue is only a fraction of the global service rate when the other queue is non-empty; when one queue is empty, the other queue has full service rate. The bivariate generating function of the queue lengths gives rise to a functional equation. In order to derive asymptotic expressions for large queue lengths, we combine the kernel method for functional equations with boundary value problems and singularity analysis.  相似文献   

10.
We prove that two independent continuous-time simple random walks on the infinite open cluster of a Bernoulli bond percolation in the lattice ?2 meet each other infinitely many times. An application to the voter model is also discussed.  相似文献   

11.
We consider a system of three arbitrary quantum particles on a three-dimensional lattice that interact via short-range attractive potentials. We obtain a formula for the number of eigenvalues in an arbitrary interval outside the essential spectrum of the three-particle discrete Schrödinger operator and find a sufficient condition for the discrete spectrum to be finite. We give an example of an application of our results.  相似文献   

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The energy operator of a system of four particles on a lattice where only two pairs of the particles interact is considered. There exist four mutually orthogonal subspaces, invariant with respect to the energy operator and such that their direct sum is equal to the entire space. The spectra of the restrictions of the energy operator to these invariant spaces are found. The dependence of the essential spectrum on the binary interaction is examined. The absence of bound states of this operator is demonstrated. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 1, pp. 81–87, April, 2000.  相似文献   

15.
In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.  相似文献   

16.
LetB n be the unit ball of ℂn and ℤ ≅ Γ ⊂ AutB n be generated by a parabolic element of AutB n. We show that the quotientB n/Γ is biholomorphic to a holomorphically convex domain of ℂn, whose automorphism group is explicity described. It follows thatB n/ℤ is Stein for any free action of ℤ. Investigation partially supported by University of Bologna. Funds for selected research topics. The second author was supported by an Instituto Nazionale di Alta Matematica grant.  相似文献   

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We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which possibly depends on the time and the latent diffusion processes, while the sampling times also possibly depend on the observed processes. In a high-frequency setting, we consider a modified version of the pre-averaged Hayashi–Yoshida estimator, and we show that such a kind of estimator has the consistency and the asymptotic mixed normality, and attains the optimal rate of convergence.  相似文献   

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We consider the family of two-particle discrete Schrödinger operators H(k) associated with the Hamiltonian of a system of two fermions on a ν-dimensional lattice ?, ν ≥, 1, where k ∈ \(\mathbb{T}^\nu \) ≡ (? π, π]ν is a two-particle quasimomentum. We prove that the operator H(k), k ∈ \(\mathbb{T}^\nu \), k ≠ 0, has an eigenvalue to the left of the essential spectrum for any dimension ν = 1, 2, ... if the operator H(0) has a virtual level (ν = 1, 2) or an eigenvalue (ν ≥ 3) at the bottom of the essential spectrum (of the two-particle continuum).  相似文献   

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