Tosomeextent，itwouldbeaccuratetosummarizethecontentsofthisbookasanintolerablyprotracteddescriptionofwhathappenswheneitheroneraisesatransitionprobabilitymatrixP(i.e.，allentries(P)oarenonnegativeandeachrowofPsumsto1)tohigherandhigherpowersoroneexponentiatesR(P-I)，whereRisadiagonalmatrixwithnon-negativeentries.Indeed，whenitcomesrightdowntoit，thatisallthatisdoneinthisbook.However，I，andothersofmyilk，wouldtakeoffenseatsuchadismissivecharacterizationofthetheoryofMarkovchainsandprocesseswithvaluesinacountablestatespace，andaprimarygoalofmineinwritingthisbookwastoconvinceitsreadersthatouroffensewouldbewarranted