(adsbygoogle = window.adsbygoogle || []).push({}); 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 L_{n}= L, u_{n}= 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

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# Brownian Motion 1 (birth-death)

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