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Multiple of Markov-chain



The Next CEO of Stack OverflowExercise on Markov chainWhy a positive recurrent Markov chain implies positive limiting probability?Finite-state Markov chainIs any subchain of Markov chain also a Markov chain?Markov chain $Z_{n+1}=max(X_n+Z_n,0)$Irreducible aperiodic Markov chainGeneral Markov propertyWhat is the name of the following (Markov-like) chain?Finding Markov Chain of $Y_n = M_n - S_n$?Definition of Markov chain












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Let $(X_n)_{ninBbb N}$ be a Markov-chain, i.e.$$forall :ninBbb N:forall:a_1,ldots,a_n,a_{n+1}inBbb Z:Bbb P(X_{n+1}=a_{n+1}mid X_n=a_n,ldots,X_1=a_1)=Bbb P(X_{n+1}=a_{n+1}mid X_n=a_n)$$
Let $pinBbb N$. How can I proof that $(X_{pcdot n})_{ninBbb N}$ is a Markov-chain again?










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    $begingroup$


    Let $(X_n)_{ninBbb N}$ be a Markov-chain, i.e.$$forall :ninBbb N:forall:a_1,ldots,a_n,a_{n+1}inBbb Z:Bbb P(X_{n+1}=a_{n+1}mid X_n=a_n,ldots,X_1=a_1)=Bbb P(X_{n+1}=a_{n+1}mid X_n=a_n)$$
    Let $pinBbb N$. How can I proof that $(X_{pcdot n})_{ninBbb N}$ is a Markov-chain again?










    share|cite|improve this question











    $endgroup$















      0












      0








      0





      $begingroup$


      Let $(X_n)_{ninBbb N}$ be a Markov-chain, i.e.$$forall :ninBbb N:forall:a_1,ldots,a_n,a_{n+1}inBbb Z:Bbb P(X_{n+1}=a_{n+1}mid X_n=a_n,ldots,X_1=a_1)=Bbb P(X_{n+1}=a_{n+1}mid X_n=a_n)$$
      Let $pinBbb N$. How can I proof that $(X_{pcdot n})_{ninBbb N}$ is a Markov-chain again?










      share|cite|improve this question











      $endgroup$




      Let $(X_n)_{ninBbb N}$ be a Markov-chain, i.e.$$forall :ninBbb N:forall:a_1,ldots,a_n,a_{n+1}inBbb Z:Bbb P(X_{n+1}=a_{n+1}mid X_n=a_n,ldots,X_1=a_1)=Bbb P(X_{n+1}=a_{n+1}mid X_n=a_n)$$
      Let $pinBbb N$. How can I proof that $(X_{pcdot n})_{ninBbb N}$ is a Markov-chain again?







      probability probability-theory markov-chains






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      share|cite|improve this question













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      share|cite|improve this question








      edited Mar 17 at 17:00







      Daniel Banov

















      asked Mar 17 at 16:55









      Daniel BanovDaniel Banov

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