Mathematics, 08.04.2020 15:28 nicole667

Let n Sn S0 Xi n 1 i1 be a simple random walk starting in the random variable S0. That is, X1, X2, . . . is a sequence of i. i.d. random variables independent of S0 such that PXi 1 p and PXi 1 1 p foralli 1 and some p 0, 1 (a) Show that ESn1Sn Sn2p1foralln0. (b) Use the result in (a) to determine for which values p 0, 1 it holds that (i) ESn 1 Sn

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Let n Sn S0 Xi n 1 i1 be a simple random walk starting in the random variable S0. That is, X1, X2, ....

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