Expectation of the stochastic process

Question

Consider the following stochastic process.

$X(t)=Y(t-1)$ where $Y(t-1)\sim Normal(X(t-1)+1,\sigma^2)$
$X(0)=1$

Now I am interested in the $E[X(n)]$. Intuitively, I think $E[X(n)]$ is equal to $n$. Is this the correct answer? If it is, how can I show this mathematically?

Is this a discrete time process? You might be able to use induction. — Sean Roberson, Dec 09 '18 at 03:33

score 2 · Accepted Answer · answered Dec 09 '18 at 03:35

2

It’s simple induction. From $E[X(t)]=E[X(t-1)]+1 $ you can easily get the desired result.

answered Dec 09 '18 at 03:35

Jack

81

Thanks! Could you elaborate little bit more? – user3509199 Dec 09 '18 at 03:47
$E[X(t)] = E[X(t-2)]+2=E[X(t-3)]+3=...=E[X(0)]+n – Jack Dec 09 '18 at 03:50

Expectation of the stochastic process

1 Answers1