REPRESENTATION OF ADDITIVE FUNCTIONALS AND LOCAL TIMES FOR JUMP MARKOV PROCESSES AND THEIR FUNCTIONAL LIMIT THEOREM

The representation of additive functionals and local times for jump Markov processes are obtained,The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.     

HILBERTIAN INVARIANCE PRINCIPLE FOR EMPIRICAL PROCESS ASSOCIATED WITH A MARKOV PROCESS

The authors establish the Hilbertian invariance principle for the empirical process of a stationary Markov process, by extending the forward-backward martingale decomposition of Lyons-Meyer-Zheng to the Hilbert space valued additive functionals associated with general non-reversible Markov processes.     

ADDITIVE FUNCTIONALS AND PERTURBATION OF SEMIGROUP

g1. Introduction and PreliminariesSuPpose that X is a right Markov process with state space E and transition sendgrouP(Pt). Given a multiplicative functional M of X, we define for any nonnegative measurablefunction f on E,Qti(x):= p"(f(X)M), x E E, t 2 0.It follows from the multiplicativity of M that (Qt) is also a semigrouP of transition functionson E and usuaJly called a perturbation semigroap of (Pt). The wellknOWn FeynmanKacsendgrouP is a special case where X is a Brownian moti…     

弱对称Markov积分半群的表示

本文研究了弱对称Markov积分半群的表示.利用积分的方法,获得了弱对称Markov积分半群的Kendall和Karlin-McGregor表示,推广了转移函数的Kendall和Karlin-McGregor表示.     

STRONG SUBORDINATION OF SYMMETRIC DIRICHLET FORMS

ＳＴＲＯＮＧＳＵＢＯＲＤＩＮＡＴＩＯＮＯＦＳＹＭＭＥＴＲＩＣＤＩＲＩＣＨＬＥＴＦＯＲＭＳＹＩＮＧＪＩＡＮＧＧＡＮＧＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＭａｙ９，１９９５．ＲｅｖｉｓｅｄＭａｒｃｈ２１，１９９６．ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈ...     

乘法分拆函数的均值估计

将正整数ｎ分拆成正整数的方法数记为ｇ（ｎ），本文对计数函数ｇ（ｎ）进行了均值估计。关于下限我们改进了［３］的结果。证明了对任意正整数ｋ皆有Σｎ≤ｘ１／ｎｇ（ｎ）≥３（４ｌｏｇ２ ｋ！２ｋ（ｋ＋１）／２）＾－１ｘｌｏｇ＾ｋｘ，ｘ≥１还获得了一个关于上限的结果Σｎ≤ｘ１／ｎｇ（ｎ）≤（ｋ－１）！Σ＾ｋ－１ｎ＝０１／ｎ！ｘ＾１／ｋ，ｘ≥１。     

马尔可夫过程H-值可加泛函的向前向后鞅分解

本文研究了马尔可夫H-值可加泛函的向前向后鞅分解.利用Lyons-Meyer-Zheng鞅分解得到了泛函数极限定理所必需的极大不等式和紧性结果,在最小条件限度内得到了马尔可夫过程经验测度的泛函中心极限定理,将该定理从实值情形推广到了希尔伯特值情形.     

THE FEYNMAN-KAC FORMULA FOR SYMMETRIC MARKOV PROCESSES

ＴＨＥＦＥＹＮＭＡＮＫＡＣＦＯＲＭＵＬＡＦＯＲＳＹＭＭＥＴＲＩＣＭＡＲＫＯＶＰＲＯＣＥＳＳＥＳＹＩＮＧＪＩＮＡＧＡＮＧＡｂｓｔｒａｃｔＬｅｔＸｂｅａｎｍｓｙｍｍｅｔｒｉｃＭａｒｋｏｖｐｒｏｃｅｓａｎｄＭａｍｕｌｔｉｐｌｉｃａｔｉｖｅｆｕｎｃ...     

Exponential transform of quadratic functional and multiplicative ergodicity of a Gauss–Markov process

The Laplace transform of partial sums of the square of a non-centered Gauss–Markov process, conditioning on its starting point, is explicitly computed. The parameters of multiplicative ergodicity are deduced.     

可列非齐次马氏链泛函的一类强大数定律

本文用分析方法研究可列非齐次马氏链的泛函的极限性质，得到了一类不同形式的强大数定律，在其中通常形式的强大数定律中的数学期望被条件期望所代替，关于独立随机变量序列的若干经典强大数定律是本文结果的推论．     

A FORMULA FOR ENERGY FUNCTIONALS

1.IntroductionInthispaperweshallestablishaformularelatingtheenergyfunctionalofarightMarkovprocesstothatofanyofitssubprocesses.LetXbearightMarkovprocessonaRadonspace(E,e)andManexactdecreasingmultiplicativefunctionalofX.Write(X,M)forthecorrespondingsubprocess,andletLandLMdenotetheenergyfunctionalsofXand(X,M)respectively.IfMdoesnotvanish,theStieltjes'logarithm[M]ofM,definedbyisanadditivefunctionalofX.WeshallprovethatforanX-dissipativemeasurefandan(X,M)-excessivefunctionu,u UIM]uisanX-…