probability theory
For a particle described by probability theory random walking on a line, the analogous thing is the list of probabilities 



(
…
,

P

−
2


,

P

−
1


,

P

0


,

P

1


,

P

2


,
…
)


{\textstyle (\ldots ,P_{-2},P_{-1},P_{0},P_{1},P_{2},\ldots )}

, which give the probability of any position. The quantities that describe how they change in time are the transition probabilities 





K

x
→
y


(
t
)



{\displaystyle \scriptstyle K_{x\rightarrow y}(t)}

, which gives the probability that, starting at x, the particle ends up at y time t later. The total probability of ending up at y is given by the sum over all the possibilities
