Study of recurrence property of jump type Markov processes

跳跃型马尔可夫过程的递推性质研究

• 批准号: 09640283
• 负责人: YAMAZATO Makoto
• 金额: $ 1.41万
• 依托单位: UNIVERSITY OF THE RYUKYUS
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640283/
• 关键词: storage process; OU type process; Levy measure; recurrence; OU型過程; オルンシュタイン=ウーレンベック型過程; ダム過程; エルゴード型

Let {A(t)} be a nonnegative subordinator without drift and r be a left continuous function on the nonnegative line to the nonnegative line with positive right limits satisfying r(O) = 0 and r(x) > 0 for x > 0. We say that a stochastic process {X(t)) is a storage process if it is determined by a stochastic differential equationdX(t) = -r(X(t))dt + dA(t)The following are our results : (a) A semigroup corresponding to the storage process is strongly continuous on the Basnach space consisting of bounded continuous functions on the nonnegative line vanishing at infinity if (I) an integral of 1/r(x) near infinity is divergent and (2) the total mass of the Levy measure is finite or the function r is nondecreasing. We determined the domain of the generator in the Case the total mass of the Levy measure is finite and gave a core for the generator in case the function r is nondecreasing. (b) We showed that the storage process is either positive recurrent or null recurrent or transient and obtained a sufficient condition for the process to be transient and a sufficient condition for the process to be recurrent. It should be remarked that 'we assume neither finiteness of the total mass of the Levy measure nor nondecreasingness of r. There are cases for which these two conditions can not be applied. However, we showed that in special case that the process Is a process of Ornstein-Uhlenbeck type, a part of the above mentioned sufficient condition for transience is sufficient for transience and it is also necessary.

设{A（t）}是一个无漂移的非负从属算子，r是一个在非负直线上的左连续函数，其右正极限满足r（0）= 0且r（x）> 0，其中x > 0.我们说一个随机过程{X（t））是一个存储过程，如果它由一个随机微分方程dX（t）= -r（X（t））dt + dA（t）决定。（a）对应于存储过程的半群在由在无穷远处消失的非负直线上的有界连续函数组成的Basnach空间上是强连续的，如果（I）1/r（x）的积分（2）Levy测度的总质量是有限的或函数r是非减的。在Levy测度的总质量有限的情况下确定了生成元的定义域，并在函数r不减的情况下给出了生成元的核. (b)证明了存储过程是正常返的、零常返的或瞬态的，并得到了存储过程是瞬态的一个充分条件和存储过程是常返的一个充分条件.应该注意的是，“我们既不假设Levy测度的总质量有限，也不假设r不减。在有些情况下，这两个条件都不能适用。然而，我们证明了在特殊情况下，该过程是一个Ornstein-Uhlenbeck型过程，上述的一部分瞬态充分条件是充分的瞬态，它也是必要的。

项目成果

M.Yamazato: "Hitting time distributions of 1-dimensional generalized diffusion" Proceedings of SAP'96. 1. 325-338 (1997)

M.Yamazato：“一维广义扩散的命中时间分布”SAP96 论文集。

C.Chen: "Robustness properties of some forecasting methods for seasonal time series:a Monte Carlo Study" International Journal of Forecasting. 13・4. 269-280 (1997)

C.Chen：“季节性时间序列的一些预测方法的稳健性：蒙特卡罗研究”《国际预测杂志》13・4（1997）。

C.CHEN: "Robustness properties of some forecasting methods for seasonal time series : A Monte Carlo study" International Journal of Forecasting. 13・2. 269-280 (1997)

C.CHEN：“季节性时间序列的一些预测方法的稳健性：蒙特卡罗研究”《国际预测杂志》13・2（1997）。

C.Chen: "Robustness properties of some forecasting methods for seasonal time series:A Monte Carlo study" International Journal of Forecasting. Vol.13・2. 269-280 (1997)

C.Chen：“季节性时间序列的一些预测方法的稳健性：蒙特卡洛研究”《国际预测杂志》第 13 卷 269-280（1997 年）。

M.Yamazato: "Recurrence-transience criteria for storage processes" Journal of Mathematical Sciences. (発表予定). (1999)

M. Yamazato：“存储过程的递归瞬态标准”数学科学杂志（即将出版）。