On the Markov property of some Brownian martingales
Let hn be the (probabilists’) Hermite polynomial of degree n. Let Hn(z,a)=an/2hn(z/a) and Hn(z,0)=zn. It is well-known that Hn(Bt,t) is a martingale for every n. In this paper, we show that for n≥3, Hn(Bt,t) is not Markovian. We then give a brief discussion on mimicking Hn(Bt,t) in the sense of constructing martingales whose marginal distributions match those of Hn(Bt,t).
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Volume (Year): 122 (2012)
Issue (Month): 10 ()
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