Exactly solvable reaction diffusion models on a Cayley tree

The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics, are discussed. Concerning the dynamics, the spectrum of the evolution Hamiltonian is found and shown to be discrete, hence there is a finite relaxation time in the evolution of the system towards its stationary state.     

Another view on martingale central limit theorems

Based on the martingale version of the Skorokhod embedding Heyde and Brown (1970) established a bound on the rate of convergence in the central limit theorem (CLT) for discrete time martingales having finite moments of order 2+2δ with 0<δ1. An extension for all δ>0 was proved in Haeusler (1988). This paper presents a rather quick access based solely on truncation, optional stopping, and prolongation techniques for martingale difference arrays to obtain other upper bounds for sup

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(φbeing the standard normal d.f.) yielding weak sufficient conditions for the asymptotic normality of . It is shown that our approach also yields two types of martingale central limit theorems with random norming.     

二参数有限随机事件流

本文讨论二参数无后效有限随机事件流的鞅性和各种二参数Ｍａｒｋｏｖ性。     

Choosing a random spanning subtree: a case study

Broder⁽⁴⁾ has suggested a stochastic algorithm for generating a random spanning subtree of a graph. This paper studies this algorithm for a special class of graphs. A complete spectral decomposition of the associated Markov chain is given. The analysis available from this is compared to stopping-time techniques and purely geometric bounds on the second eigenvalue.     

Asymptotic distribution of maximal autoregressive process with weight tending to 1

The maximal operator plays the similar role as the summation operator in the sense of stability of operation. So, we could discussARMA processes in the maximal operation by the same way as in the summation operation. However, many papers already treated with moving order statistics. In this paper, we discuss asymptotic behaviors of maximal autoregressive (MAR) processes with the weight tending to 1.     

Poisson convergence in the restricted k‐partitioning problem

The randomized k‐number partitioning problem is the task to distribute N i.i.d. random variables into k groups in such a way that the sums of the variables in each group are as similar as possible. The restricted k‐partitioning problem refers to the case where the number of elements in each group is fixed to N/k. In the case k = 2 it has been shown that the properly rescaled differences of the two sums in the close to optimal partitions converge to a Poisson point process, as if they were independent random variables. We generalize this result to the case k > 2 in the restricted problem and show that the vector of differences between the k sums converges to a k ‐ 1‐dimensional Poisson point process. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

A two-sided estimate in the Hsu-Robbins-Erdös law of large numbers

Let X₁, X₂, … be independent identically distributed random variables. Then, Hsu and Robbins (1947) together with Erdös (1949, 1950) have proved that

,

if and only if E[X²₁] < ∞ and E[X₁] = 0. We prove that there are absolute constants C₁, C₂ (0, ∞) such that if X₁, X₂, … are independent identically distributed mean zero random variables, then

c₁λ⁻² E[X₁²·1_{|X1|λ}]S(λ)C₂λ⁻² E[X₁²·1_{|X1|λ}]

,

for every λ > 0.     

The multifractal spectrum of statistically self-similar measures

We calculate the multifractal spectrum of a random measure constructed using a statistically self-similar process. We show that with probability one there is a multifractal decomposition analogous to that in the deterministic self-similar case, with the exponents given by the solution of an expectation equation.     

Minimal Martingale Measures for Discrete-time Incomplete Financial Markets

Abstract In this note, we give a characterization of the minimal martingale measure for a general discrete-time incomplete financial market.Then we concretely work out the minimal martingale messure for a specificdiscrete-time market model in which the assets'returns in different times are independent.     

A note on the projecton of Gibbs measures

We give an example of a projection which maps two Gibbs measures for the same interaction into Gibbs measures for different interactions. As a corollary we find a case where by decimation a non-Gibbsian measure is transformed into a Gibbs measure.