ERRATUM TO： LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION （ACTA MATHEMATICA SCIENTIA 2016,36B （2） ：394-408）

我们给定理 2.2 沈，殷和 Yan (2016 ) 的修正。

LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION

In this article, we study a least squares estimator(LSE) of θ for the OrnsteinUhlenbeck process X_0=0, dX_t =θX_tdt + dB_t^(a,b), t≥ 0 driven by weighted fractional Brownian motion B^(a,b) with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {X_s, s ∈ [0, t]} as t tends to infinity.

Reflected BSDEs Driven by Lévy Processes and Countable Brownian Motions

A new class of reflected backward stochastic differential equations (RBSDEs) driven by Teugels martingales associated with Lévy process and Countable Brownian Motions are investigated. Via approximation, the existence and uniqueness of solution to this kind of RBSDEs are obtained.

一个广义Brownian Sheet函数的概率分布估计

本文采用与[2]不同的方法,得到了广义Brownian Sheet在矩形域上的最大值的尾分布估计,以及包括[2]中“对称原理”在内的广义Brownian Sheet函数的概率分布估计。

广义Brownian Sheet的马氏性、转移概率和预测

讨论了广义BrownianSheet的单点马氏性、宽过去马氏性、宽将来马氏性、*-马氏性,各种转移概率及其预测.

分数CIR过程统计行为的数值模拟

Cox-Ingersoll-Ross (CIR)过程在金融领域有着重要的应用,本文主要对分数CIR过程的统计行为进行了模拟和探讨.由于该过程不存在解析解,拟采用两种不同随机函数wfbm和fbmld来模拟分数布朗运动,利用Euler-Maruyama (EM)方法模拟分数CIR过程的期望和方差.由于分数CIR过程的分布不能用福克–普朗克方程(Fokker-Planck equation)的解来表示,文章模拟了分数CIR过程的经验分布,并得到了随时间变化时的经验分布变化情况.为了进一步验证该Euler-Maruyama(EM)算法和比较两种随机函数的优越性,模拟了可以转化为向后欧拉法的分数Cox-Ingersoll-Ross(CIR)模型和具有解析解的分数Ornstein-Uhlenbeck (OU)模型,通过比较图像和数据,发现采用函数fbmld模拟的分数CIR过程的期望以及方差和理论上的期望以及方差具有较强的拟合程度.

关于Brownian粒子速度的一个指数型估计

本文研究出发于零点的一维Brownian粒子速度的一种指数型估计。这种粒子的速度是Langevin方程的唯一平稳解,它也可由时间齐次线性Fokker-Planck方程来刻画。我们利用停时的对数矩,给出了这个轨道过程的一种指数可积性的充分必要条件。

LINEAR SEARCH FOR A BROWNIAN TARGET MOTION

A target is assumed to move according to a Brownian motion on the real line.The searcher starts from the origin and moves in the two directions from the starting point.The object is to detect the target.The purpose of this paper is to find the conditions under which the expected value of the first meeting time of the searcher and the target is finite,and to show the existence of a search plan which made this expected value minimum.

RUIN PROBLEM FOR A CLASS OF RISK PROCESSES PERTURBED BY DIFFUSION

In this paper,a class of risk processes perturbed by diffusion are considered. The Lundberg inequalities for the ruin probability are obtained.The size of the Lundberg exponents for different kinds of risk model is compared. The numerical illustration for the impact of the parameters on the ruin probability is given.

Production sharing contract: An analysis based on an oil price stochastic process

Assuming that oil price follows the stochastic processes of Geometric Brownian Motion (GBM) or the Mean-Reverting Process (MRP), this paper takes the net present value (NPV) as an economic index and models the PSC in 11 different scenarios by changing the value of each contract element (i.e. royalty, cost oil, profit oil as well as income tax). Then the NPVs are shown in probability density graphs to investigate the effect of different elements on contract economics. The results show that under oil price uncertainty the influence of profit oil and income tax on NPV are more significant than those of royalty and cost oil, while a tax holiday could improve the contractor's financial status remarkably. Results also show that MRP is more appropriate for cases with low future oil price volatility, and GBM is best for high future oil price volatility.

A LIMINF RESULT FOR HANSON-RUSSO TYPE INCREMENTS OF FRACTIONAL BROWNIAN MOTION

Let {X(t), t > 0} be a fractional Brownian motion of order 2α with 0 < α <1,β > 0 be a real number, aT be a function of T and 0 < aT< T, lim(log T/aT)/log log T = r, (0 < r<∞). In this paper, we proved thatwhere c1, c2 are two positive constants depending only on α,β.

On the sub-mixed fractional Brownian motion

Let {SHt, t ≥ 0} be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 < H < 1. Its main properties are studied.They suggest that SHlies between the sub-fractional Brownian motion and the mixed fractional Brownian motion. We also determine the values of H for which SHis not a semi-martingale.

STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS

让 { Xt ≥ 1 } 一个动人的平均过程被在哪儿定义 { ak k ≥ 0 } 是实数的一个序列并且 { t，∞ < t < ∞ } 是严格地静止的依赖随机的变量的一个二倍地无限的序列。在条件下面 { ak k ≥ 0 } 它必要那 { Xt， t ≥ 1 } 是长存储器进程或线性进程，强壮的近似 { Xt， t ≥ 1 } 到 Gaussian，进程被学习。最后，结果被使用为动人的平均过程获得一个长记忆过程的强壮的近似到一个部分 Brownian 运动和重申的对数的法律。

The Multifractal Analysis of the Occupation Measure of a Lévy Process

WT5”HZ]We introduced the results on the multifractal structure of the occupation measures of a Brownian Motion, a stable process, a general subordinator and a stochastic process derived from random reordering of the Cantor set. We also introduced an interesting and powerful technique to investigate the multifractal spectrum. [WT5HZ]

First exit distribution and path continuity of Hunt processes

This paper gives a characterization of a Hunt process path by the first exit left limit distribution.It is also showed that if the first exit left limit distribution leaving any ball from the center is a uniform distribution on the sphere,then the L'evy Processes are a scaled Brownian motion.

Current and efficiency of Brownian particles under oscillating forces in entropic barriers

In this study, considering the temporarily unbiased force and different forms of oscillating forces, we investigate the current and efficiency of Brownian particles in an entropic tube structure and present the numerically obtained results.We show that different force forms give rise to different current and efficiency profiles in different optimized parameter intervals. We find that an unbiased oscillating force and an unbiased temporal force lead to the current and efficiency,which are dependent on these parameters. We also observe that the current and efficiency caused by temporal and different oscillating forces have maximum and minimum values in different parameter intervals. We conclude that the current or efficiency can be controlled dynamically by adjusting the parameters of entropic barriers and applied force.

Strong Local Non-Determinism of Sub-Fractional Brownian Motion

Let be a subfractional Brownian motion in . We prove that is strongly locally nondeterministic.

Existence and joint continuity of local time of multi-parameter fractional Lévy processes

In this paper,we introduce the definition of a multi-parameter fractional Lévy process and its local time,and show its decomposition.Using the decomposition,we prove existence and joint continuity of its local time.

REMARKS ON SUB-FRACTIONAL BESSEL PROCESSES

Let S = {(St1,···,Std )}t≥0 denote a d-dimensional sub-fractional Brownian motion with index H ≥ 1/2. In this paper we study some properties of the process X of the formwhere Rt = ((St1)2+···+(Std)2)~1/2 is the sub-fractional Bessel process.

THE JOINT DISTRIBUTIONS OF SOME ACTUARIAL DIAGNOSTICS FOR THE JUMP-DIFFUSION RISK PROCESS

In this article, the joint distributions of several actuarial diagnostics which are important to insurers’ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately (simply, the ultimately leaving-time), the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of L′evy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.