Equations ( 1 ) - ( 5 ) hold for any 1D semi-Markovian random walk in a L - state chain .
Equations ( 1 ) - ( 5 ) form the most general solution in an explicit form for random walks in 1d .
Equations ( 1 ) - ( 5 ) hold for any 1D semi-Markovian random walk in a L - state chain , and form the most general solution in an explicit form for random walks in 1d .