On the Markov property of some Brownian martingales

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Fan, J. Y.¹  Hamza, K.¹  Klebaner, F. C.¹ 

[1] Monash Univ, Sch Math Sci, Clayton, Vic 3800, Australia

关键词: Brownian martingales;    Hermite polynomials;    Markov property;    Mimicking selfsimilar martingales;   

DOI  :  10.1016/j.spa.2012.06.004

来源: Elsevier

【 摘 要 】

Let h(n) be the (probabilists') Hermite polynomial of degree n. Let H-n(z, a) = a(n/2)h(n)(z/root a) and H-n(z, 0) = z(n). It is well-known that H-n(B-t, t) is a martingale for every n. In this paper, we show that for n >= 3, H-n (B-t, t) is not Markovian. We then give a brief discussion on mimicking H-n(B-t, t) in the sense of constructing martingales whose marginal distributions match those of H-n(B-t, t). (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free