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PDF-MathematicalIdeasUnderstandingaStochasticProcessWeconsiderasequenceofB PDF document

qpa1ifp6qandqT01T0aifpq123 ProofAfterthe rsttrialthegamblersfortuneiseitherT01orT01andthereforewemusthaveqT0pqT01qqT011provided1T0a1ForT01the rsttrialmayleadtoruinand1isre

(q=p)a1ifp6=qandqT0=1T0=aifp=q=1=2.3 Proof.Afterthe rsttrialthegambler'sfortuneiseitherT01orT0+1andthereforewemusthaveqT0=pqT0+1+qqT01(1)provided1T0a1.ForT0=1 the rsttrialmayleadtoruin and(1)isre

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