# Let N(t) be a Poisson Process with constant intensity on R.?

(a) find the covariance of N(s) and N(t)

(b) show that N is continuous in mean square, which is to say that E[{N(t+h)-N(t)}^2]

-->0 as h-->0.

(c) prove that N is continuous on probability, which is to say that P(|N(t+h)-N(t)|>∈)->0

as h-->0, for all ∈>0

(d) Show that N is differentiable in probability but not in mean square.

### 1 Answer

Relevance

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