- #1
tyler_T
- 17
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Problem:
Let X(t), t>0 denote the birth and death process that is allowed to go negative and that has constant birth and death rates Ln = L, un = u (n is integer). Define u and c as functions of L in such a way that cX(t), t>u converges to Brownian motion as L approaches infinity.
Attempt at solution:
Since the expected value of cX(t), must equal 0, it is obvious that u = L.
The answer to the second part is c = 1/sqrt(2L), but I have no idea how to get there.
Can anybody help me make sense of this?
-Tyler
Let X(t), t>0 denote the birth and death process that is allowed to go negative and that has constant birth and death rates Ln = L, un = u (n is integer). Define u and c as functions of L in such a way that cX(t), t>u converges to Brownian motion as L approaches infinity.
Attempt at solution:
Since the expected value of cX(t), must equal 0, it is obvious that u = L.
The answer to the second part is c = 1/sqrt(2L), but I have no idea how to get there.
Can anybody help me make sense of this?
-Tyler