Strong Approximation for Long Memory Processes with Applications

In this paper we inverstigate the strong approximation of a linear process with long memory to a Gaussian process. The results are then applied to derive the law of the iterated logarithm and Darling–Erds type theorem for long memory processes under ideal conditions.     

非时齐马氏过程的Liggett-Stroock不等式

本文将时齐马氏过程中重要的代数不等式Liggett-Stroock不等式推广到非时齐马氏过程中,建立了非时齐马氏过程的转移半群与Liggett-Stroock不等式之间的关系.     

Infinite Divisibility for Stochastic Processes and Time Change

General results concerning infinite divisibility, selfdecomposability, and the class L _m property as properties of stochastic processes are presented. A new concept called temporal selfdecomposability of stochastic processes is introduced. Lévy processes, additive processes, selfsimilar processes, and stationary processes of Ornstein–Uhlenbeck type are studied in relation to these concepts. Further, time change of stochastic processes is studied, where chronometers (stochastic processes that serve to change time) and base processes (processes to be time-changed) are independent but do not, in general, have independent increments. Conditions for inheritance of infinite divisibility and selfdecomposability under time change are given.     

Asymptotics of Intersection Local Time for Diffusion Processes

In the paper, we investigate the intersection local time for two correlated Brownian motions on the plane that form a diffusion process in ?⁴ associated with a divergence-form generator. Using Gaussian heat kernel bounds, we prove the existence of intersection local time for these Brownian motions, obtain estimates of its moments, and establish the law of iterated logarithm for it.

     

Particle Finite Element Simulations of Cutting Processes in Manufacturing

The cutting of metals is an important process in manufacturing and challenges established methods in the field of computational mechanics. The particle finite element method (PFEM) combines the benefits of particle based methods and the standard finite element method (FEM) to account for large deformations and separation of material. In cutting simulations the workpiece is realised as a set of particles, whose boundary is detected by the α-shape method. After the boundary detection, the particles are meshed with finite elements. Since metals show a plastic behavior under large deformations, a suitable material model needs to be considered. Numerical examples show the effect of the choice of the parameter α on the cutting force. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimation of Local Smoothness Coefficients for Continuous Time Processes

We consider processes that satisfied a local Hölder condition with coefficient ₀. According to the sampling times of observations given by i _n with i=0,...,n–1, we study two general classes of estimators for ₀. Their almost sure rates of convergence depend on asymptotic independence of the observed processes, on _n and eventually on an extra parameter ₀. Since this last parameter is in general unknown, we construct a family of preliminary estimators for ₀ with their rates of almost sure convergence. Finally we present some numerical simulations in order to compare the behaviour of our various estimators.     

离散时间马氏链的L~2几何收敛

对于离散时间马氏链,转移概率矩阵P关于平稳分布可逆的条件下,给出过程L2几何收敛速率与谱隙之间的关系,并得到最优L2几何收敛速率与最优几何遍历速率的一致性.     

Stopping Time Convergence for Processes Associated with Dirichlet Forms

Potential Analysis - Convergence is proved for solutions un of Dirichlet problems in regions with many small excluded sets (holes), as the holes become smaller and more numerous. The problem is...     

Boundary Sensitivities for Diffusion Processes in Time Dependent Domains

We study the sensitivity, with respect to a time dependent domain of expectations of functionals of a diffusion process stopped at the exit from or normally reflected at the boundary of We establish a differentiability result and give an explicit expression for the gradient that allows the gradient to be computed by Monte Carlo methods. Applications to optimal stopping problems and pricing of American options, to singular stochastic control and others are discussed.     

Hitting Time Distributions for Denumerable Birth and Death Processes

For an ergodic continuous-time birth and death process on the nonnegative integers, a well-known theorem states that the hitting time T _0,n starting from state 0 to state n has the same distribution as the sum of n independent exponential random variables. Firstly, we generalize this theorem to an absorbing birth and death process (say, with state ?1 absorbing) to derive the distribution of T _0,n . We then give explicit formulas for Laplace transforms of hitting times between any two states for an ergodic or absorbing birth and death process. Secondly, these results are all extended to birth and death processes on the nonnegative integers with ?? an exit, entrance, or regular boundary. Finally, we apply these formulas to fastest strong stationary times for strongly ergodic birth and death processes.     

Some Eigen Theory Results for Moving Average Time Processes

Some theoretical eigen properties of moving average time processesare deduced and an unsolved problem is posed.     

Quasi-Stationary Asymptotics for Perturbed Semi-Markov Processes in Discrete Time

We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in addition, one absorbing state. Our main object of interest is the asymptotic behavior of the joint probabilities of the position of the semi-Markov process and the event of non-absorption as time tends to infinity and the perturbation parameter tends to zero. The main result gives exponential expansions of these probabilities together with a recursive algorithm for computing the coefficients in the expansions. An application to perturbed epidemic SIS models is discussed.     

On Realizations from Nonstationary Time Processes

Unthinking inferences from the sampled autocorrelation structure, for realisations of certain nonstationary processes, can lead to misguided identifications and, possibly, misleading fits. Effective time-series modelling must include inspection of the raw data, and will often also depend on extraneous information available to the analyst.     

Near-invariant Tori on Exponentially Long Time for Poisson systems

This paper deals with the near-invariant tori for Poisson systems. It is shown that the orbits with the initial points near the Diophantine torus approach some quasi-periodic orbits over an extremely long time. In particular, the results hold for the classical Hamiltonian system, and in this case the drift of the motions is smaller than one in the past works.     

Remarks on Estimation Problem for Stationary Processes in Continuous Time

The problem of estimating of the law (in the space of the paths) and the common marginal distribution for a strictly stationary ergodic process X is discussed. We show, in particular, that:(1) The empirical measure

Variational Approach for Learning Markov Processes from Time Series Data

Journal of Nonlinear Science - Inference, prediction, and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management,...