The improved LaSalle-type theorems for stochastic functional differential equations

The main aim of this paper is to improve some results obtained by Mao [X. Mao, The LaSalle-type theorems for stochastic functional differential equations, Nonlinear Stud. 7 (2000) 307-328]. Our new theorems give better results while conditions imposed are much weaker than in the paper mentioned above. For example, we need only the local Lipschitz condition but neither the linear growth condition nor the bounded moment condition on the solutions. To guarantee the existence and uniqueness of the global solution to the underlying stochastic functional differential equation (SFDE) under the weaker conditions imposed in this paper, we establish a generalised existence-and-uniqueness theorem which covers a wider class of nonlinear SFDEs as demonstrated by the examples discussed in this paper. Moreover, from our improved results follow some new criteria on the stochastic asymptotic stability for SFDEs.     

Asymptotic Stability and Boundedness of Stochastic Differential Equations with Respect to Semimartingales

In this paper, we shall use multiple Lyapunov functions to establish some sufficient criteria for locating the limit sets of solutions of stochastic differential equations with respect to semimartingales. From them follow many useful results on stochastic asymptotic stability and boundedness, including some classical results as special cases. In particular, our new asymptotic stability criteria do not require the diffusion operator associated with the underlying stochastic differential equation be negative definite, while most of the existing results do require this negative definite property essentially.     

Attraction and Stochastic Asymptotic Stability and Boundedness of Stochastic Functional Differential Equations with Respect to Semimartingales

Abstract

In this paper, we will establish new results on the attraction for solutions to stochastic functional differential equations with respect to semimartingale. Most of the existing results stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in the study of attraction. Moreover, from our results on the attraction follow several new criteria on almost surely asymptotic stability and boundedness of the solutions.     

延拓分支过程

本给出一类连续时间延拓分支过程Ｘ（ｔ）的大偏差原理成立的条件以及有关的一类上鞅。     

A generalized JM model with applications to imperfect debugging in software reliability

For their nice mathematical properties, state space models have been widely used, especially for forecasting. Over the last decades, the study of tracking software reliability by statistical models has attracted scientists’ attention. However, most of models focus on perfect debugging although practically imperfect debugging arises everywhere. In this paper, a non-Gaussian state space model is modified to predict software failure time with imperfect debugging. In fact, this model is very flexible so that we can modify the system equation in this model to satisfy the various situations. Besides, this model is suitable for tracking software reliability, and applied to two well known datasets on software failures.     

THE OPTIMAL STOPPING PROBLEM OF A CONTINUOUS PARAMETER PROCESS

Suppose X = (Xr, Fr, t ∈ R+) be an optional reward process with ( Fr) satisfying usual conditions. In this paper, we correct the proof of existence about Snell envelope in [4] and the proof of an important lemma (Lemma 4. 6) in [5], and give a proof of existence about Snell envelope under certain conditions, i. e. EZx- < ∞ and Z is upper-semi-continuous on the right (USCR) or there is a stopping rule (SR)τ ≤σ such that EZx-∞ for any stopping rule σ . At the same time, we prove a four-repeated limit theorem when Z is continuous on the right. The character and the uniqueness of the optimal stopping time (OST) or optimal stopping rule (OSR) are discussed.     

On the semimartingale property of discounted asset-price processes

A financial market model where agents trade using realistic combinations of simple (i.e., finite combinations of buy-and-hold) no-short-sales strategies is considered. Minimal assumptions are made on the discounted asset-price process — in particular, the semimartingale property is not assumed. Via a natural market viability assumption, namely, absence of arbitrage of the first kind, we establish that discounted asset-prices have to be semimartingales. Our main result can also be regarded as reminiscent of the Fundamental Theorem of Asset Pricing.     

起空间P_(bfc)(X)中新的半序及其应用(英语)

当X是一可分Banach格时,本文建立了单点值上鞅的集值序上鞅理论。     

Recurrency and Transiency of Markov Processes Governed by Coupled Systems of Second–Order Elliptic Operators

Markov processes corresponding to coupled systems of the form k=1,2,...,m, are considered. Here L_k are second–order linear elliptic operators and d_k,j are non–negative functions. We prove sufficient conditions for the recurrency and transiency of the Markov processes corresponding to such systems and alos provide some examples which show that it is possible to have a recurrent system even if some or all its components are transient; where by components, we mean the Markov processes engendered by the uncoupled equations. We also provide all example which shows that a system composed of recurrent processes may itself be transient. Finally, we consider necessary and sufficient conditions for the exterior Dirichlet problem of the coupled system to have a bounded solution as.