On the Markov property of some Brownian martingales

J.Y. Fan, K. Hamza and F.C. Klebaner

Stochastic Processes and their Applications, 2012, vol. 122, issue 10, 3506-3512

Abstract: 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).

Keywords: Brownian martingales; Hermite polynomials; Markov property; Mimicking selfsimilar martingales (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spa.2012.06.004

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