 About 6,940 results  books.google.com If a stochastic matrix is indecomposable and if the class of positive states of the
Markov chain has period d. then the set of ... v (see also Markov chain, ergodic:
for infinite stochastic matrices P, the system of equations (1) may have no non
zero ... 

 books.google.com Recall that r ij is the expected number of times that state j is visited, given that the
Markov chain starts in state i. State i is recurrent ... If transient state i cannot reach
any state of recurrent class C(j), then rik = 0 for all k ∈ C(j). Thus, given that i is ... 

 books.google.com 01 m 2 1 2 m i O O O O O 16.5 23 0 : transitions between non−essential states :
transitions from non−essential states to the i th closed class : transitions C i inside
the i th closed class O Fig. 1.4 Let us now go back to finitestate Markov chains In
... 

 books.google.com It is clear that if a state x(i) is reachable from x(j) (x(j) =$• x(i}) and, in turn, a state x
(k) is reachable from x(i) (x(i) => x(k)) ... to remain in state x(i] is positive, and the
probability to move from any state x(j), j ^ i, to tfie state x(i) is equal to zero.
Definition 15 The class X (i) is said to be the jth communicating class of states if it
includes all communicating states of a given finite Markov, i.e., it includes all
states such ... 

 books.google.com Markov. Chain. Theory. A discretetime Markov process on a finite state space Z
specifies the probability of transiting to each state in Z ... Specifically, for every
pair of states z, z' ∊ Z, and every time t > 0, let Pzz'(t) be the transition probability
of moving to state z' at time t + 1 conditional on being in state 2 at time t . ... It is
straightforward to show that every finite Markov chain has at least one recurrent
class. 

 books.google.com (3.25) n=0 We would like now to introduce some types of regularity of a SMC (
MRC) using a description of the states. To this ... The semiMarkov chain (Markov
renewal chain) is said to be irreducible if there is only one class. 3. A state i is
said ... 

 books.google.com Thus we can classify the states In] of a Markov chain according to the sequence
of nstep probabilities {PM These are shown in Table 5.2. lrreducible Markov
Chains I'll State] is reachable from state i if PM > 0 for some n. ... A set of states
such that every pair of states inside the class communicate with each other, and
no state outside the set is reachable from inside the set, is called a
communicating class ... 

 books.google.com The matrix P is the transition matrix of the Markov chain that models the random
walk on E. The importance of a Web page is related to the ... E there corresponds
a vertex of the digraph and one defines a directed arc from vertex i to vertex j for
each pair of states such that pi,j > 0 ... The strongly connected components of the
transition graph are the communicating classes of states, or of the Markov chain. 

 books.google.com The matrix P is the transition matrix of the Markov chain that models the random
walk on E. The importance of a Web page is related to the probability of reaching
such ... the digraph and one defines a directed arc from vertex i to vertex j for
each pair of states such that pi,j > 0. ... The strongly connected components of the
transition graph are the communicating classes of states, or of the Markov chain. 

 books.google.com T T R T T v Uq Ug Uq Uq = − = − = (4.145) Thus, if the rewards received in all the
recurrent states are set equal to zero, ... rewards received before passage to a
closed class of recurrent states, given that the chain started in a transient state, ... 

 