Recurrent Class: Set of state inA(i)form a recurrent class. States inA(i)are accessible from each other, no states outsideA(j)is accessible from them. For a recurrent statei, we haveA(i)=A(j)ifjbelongs toA(i). And we drived the Markov chain decomposition law: A Markov chain can ...
如果状态 i 是recurrent states,那么 A(i) 集合(recurrent class)里所有的状态是互相可达的。 马尔可夫链分解: 一条马尔可夫链可以分解成多个recurrent class,以及其他一些transient states; \forall k\in A(i),\ r_{ki}(n)>0 ,即从任何该recurrent class的状态出发都可以到达状态 i; 任何一个recurrent cl...
5 - 2 - 3-1-1 From States to Markov Chain (english version) 从状态到马尔可夫链 (英文版) [08-, 视频播放量 27、弹幕量 0、点赞数 0、投硬币枚数 0、收藏人数 0、转发人数 0, 视频作者 Googleplex, 作者简介 曾经沧海难为水,相关视频:2 - 2 - 1-2-1 Essential Concept
The meaning of MARKOV CHAIN is a usually discrete stochastic process (such as a random walk) in which the probabilities of occurrence of various future states depend only on the present state of the system or on the immediately preceding state and not on
markov_chains
is either that the Markov chain is wandering off to infinity, if one enumerates the states in any arbitrary way, or that it visits all the states infinitely often but makes such large excursions in the state space that it spends a negligible fraction of time in any finite set of states....
马尔可夫过程 (Markov process) 指具有马尔可夫性质的随机过程,也被称为马尔可夫链 (Markov chain) 。我们通常用元组 描述一个马尔可夫过程,其中 是 有限数量的状态集合, 是状态转移矩阵 (state transition matrix)。假设一共有 个状态,此时 。 状态转移矩阵 定义了所有状态对之间的转移 概率,即 矩阵 中第 行第 ...
As we progress through time, theprobability of being in certain states are more likely than others. Over the long run, the distribution will reach anequilibriumwith an associated probability of being in each state. This is known as theStationary Distribution. ...
That is, we suppose that (4.1.1) P{Xn+1=j Xn-1=in-1,...,X1=i1,X0=i0}=Pij for all states i0 ,i1,...in-1 , i, j and all n ≥0.Such a stochastic process is known as a Markov chain. Equation(4.1.1)may be interpreted as stating that, for a Markov chain,the ...
Consider a Markov chain with a single recurrent class, which is aperiodic. Then, the states j are associated with steady-state probabilities \pi_{j} that have the following properties.(非周期:非震荡,会收敛) (a) For each j , we have(非周期单一循环类的情况下,无论出发状态,到指定的状态随着...