Solutions to boundary Cauchy problems with infinite delay

In this paper, we investigate the existence, uniqueness of solutions to boundary Cauchy equations with infinite delay, which are more general than the previous studies. The conclusions are applied to an age dependent population with delay in the birth process.     

双曲正弦和双曲余弦函数的幂级数余项的不等式

该文建立了双曲正弦和双曲余弦函数的幂级数余项的若干不等式.     

Transportation distances and noise sensitivity of multiplicative Lévy SDE with applications

This article assesses the distance between the laws of stochastic differential equations with multiplicative Lévy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Lévy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.     

Time change equations for Lévy-type processes

We consider time change equations for Lévy-type processes. In this context we generalize the results of Böttcher et al. (2013) significantly. Namely, we are able to incorporate measurable instead of continuous multipliers. This opens a gate to find whole classes of symbols for which corresponding processes do exist. In order to establish our results we carefully analyze the connection between time change equations and classical initial value problems. This relationship allows us to transfer well-known results from this classical subject of pure mathematics into the theory of stochastic processes. On the way to prove our main theorem we establish generalizations of results on paths of Lévy-type processes.     

A note on demand functions with uncertainty

Demand functions with “additive” and “multiplicative” uncertainty can fail to satisfy the “Slutsky symmetry” conditions required for demand to be based on utility maximization. This makes welfare analysis infeasible, which is important in many applications. Additive uncertainty can also generate negative demand realizations, and this can create non-trivial analytical problems.     

Matrix characterization of A-statistical convergence

The main objective of the paper is to characterize multipliers of summability fields of regular methods, while relaxing the usual boundedness condition. For this purpose we use the sequence spaces of A-bounded sequences and A-uniformly integrable sequences. Among the main results, it is shown that the space of multipliers is closely related to the space of A-statistically convergent sequences and that A-statistical convergence over ?_∞ is equivalent to a regular matrix method. This observation eliminates the need for separate proofs of several A-statistical convergence results.     

An efficient approach to updating simplex multipliers in the simplex algorithm

The simplex algorithm computes the simplex multipliers by solving a system (or two triangular systems) at each iteration. This note offers an efficient approach to updating the simplex multipliers in conjunction with the Bartels–Golub and Forrest–Tomlin updates for LU factors of the basis. It only solves one triangular system. The approach was implemented within and tested against MINOS 5.51 on 129 problems from Netlib, Kennington and BPMPD. Computational results show that the new approach improves simplex implementations. Project 10371017 supported by National Natural Science Foundation of China.     

乘代数重建法和最大熵重建法比较研究

本文从最大熵原理引入拉格朗日因子推导出乘代数重建法(MART)和最大熵重建法(MENT),同时他们是等价的,只是迭代方法不同而已。而且用实例进行模拟计算,计算结果也表明这两种方法收敛情况和重建精度完全一致,从而进一步证明MART和MENT的等价性。     

Weak order stochastic Runge–Kutta methods for commutative stochastic differential equations

A new explicit stochastic Runge–Kutta scheme of weak order 2 is proposed under a commutativity condition, which is derivative-free and which attains order 4 for ordinary differential equations. The weak order conditions are derived by utilizing multi-colored rooted tree analysis and a solution is found in a transparent way. The scheme is compared with other derivative-free and weak second order schemes in numerical experiments.     

Stationary and dynamical properties of finite N-unit Langevin models subjected to multiplicative noises

We have studied the finite N-unit Langevin model subjected to multiplicative noises, by using the augmented moment method (AMM), as a continuation of our previous paper [H. Hasegawa, J. Phys. Soc. Japan 75 (2006) 033001]. Effects of couplings on stationary and dynamical properties of the model have been investigated. The difference and similarity between the results of diffusive and sigmoid couplings are studied in details. Time dependences of average and fluctuations in local and global variables calculated by the AMM are in good agreement with those of direct simulations (DSs). We also discuss stationary distributions of local and global variables with the use of the Fokker–Planck equation (FPE) method and DSs. It is demonstrated that stationary distributions show much variety when multiplicative noise and external inputs are taken into account.