Markov Chains Chapter 3

Discussion in 'CT4' started by Harashima Senju, Oct 14, 2014.

  1. Harashima Senju

    Harashima Senju Ton up Member

    I do not understand model 5.3 Simple Random Walk

    $$P[X_n=j|X_1=i_1,...,X_{m-1}=i_{m-1},X_m=i_m]$$
    =$$P[X_m+Y_{m+1}+...+Y_n=j|X_1=i_1,...,X_{m-1}=i_{m-1},X_m=i_m]$$
    How do you arrive at the second step
     
    Harashima Senju, Oct 14, 2014
    #1
  2. Hemant Rupani

    Hemant Rupani Senior Member

    X_n is the SUM(i =1 to n ) of Y_i

    X_m is the SUM(i =1 to m) of Y_i

    So X_n = X_m + SUM( i =m+1 to n) of Y_i
     
    Hemant Rupani, Oct 14, 2014
    #2
  3. Harashima Senju

    Harashima Senju Ton up Member

    Thanks
     
    Harashima Senju, Oct 14, 2014
    #3

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