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References
- Andersen, T.G., Bollerslev, T., Diebold, F.X. and Labys, P., Modelling and Forecasting Realized Volatility. Econometrica 71, pp. 579-625, 2003. Math. Review 1958138
- Andersen, T.G., Bollerslev, T. and Dobrev, D., No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: theory and testable distributional implications. J. Econometrics 138, pp. 125-180, 2007. Math. Review 2380695
- Athreya, K.B. and Ney, P.E., Branching Processes. Springer, 1972. Math. Review 0373040
- Barlow, M., Random walks, electrical resistance and nested fractals. In: Elworthy, K.D. and Ikeda, N. (Eds.), Asymptotic problems in probability theory: stochastic models and diffusions on fractals. Pitman, Montreal, pp. 131-157, 1993. Math. Review 1354153
- Barlow, M.T. and Perkins, E.A., Brownian motion on the Sierpinski gasket. Probab. Theory Related Fields 79, pp. 543-623, 1988. Math. Review 0966175
- Chainais, P., Riedi, R. and Abry, P., Scale invariant infinitely divisible cascades. In: Int. Symp. on Physics in Signal and Image Processing, Grenoble, France, 2003. Math. Review number not available.
- Dambis, K.E., On decomposition of continuous submartingales. Teor. Verojatnost. i Primenen. 10, pp. 438-448, 1965. Math. Review 0202179
- Decrouez, G. and Jones, O.D., A class of multifractal processes constructed using an embedded branching process. Preprint, 2011.
- Dubins, L. and Schwarz, G., On continuous martingales. Proc. Nat. Acad. Sci. USA 53, pp. 913-916, 1965. Math. Review 0178499
- Guasoni, P., Excursions in the martingale hypothesis. In: Akahori, J., Ogawa, S. and Watanabe, S. (Eds.), Stochastic Processes and Applications in Mathematical Finance. World Scientific, pp. 73-96, 2004. Math. Review 2202693
- Heyde, C., A risky asset model with strong dependence through fractal activity time. J. Appl. Probab. 36, pp. 1234-1239, 1999. Math. Review 1746407
- Hull, J. and White, A., The pricing of options on assets with stochastic volatilities. J. Finance 42, pp. 281-300, 1987. Math. Review number not available.
- Jones, O.D. and Rolls, D.A., Looking for continuous local martingales with the crossing tree (Working Paper), 2009. arXiv:0911.5204v2 [math.ST]
- Jones, O.D. and Shen, Y., Estimating the Hurst index of a self-similar process via the crossing tree. Signal Processing Letters 11, pp. 416-419, 2004. Math. Review number not available.
- Knight, F.B., On the random walk and Brownian motion. Trans. Amer. Math. Soc. 103, pp. 218-228, 1962. Math. Review 0139211
- Knight, F.B., Essentials of Brownian motion and diffusion. Mathematical Surveys 18, Amer. Math. Soc., 1981. Math. Review 0613983
- Le Gall, J-F., Brownian excursions, trees and measure-valued branching processes. Ann. Probab. 19, pp. 1399-1439, 1991. Math. Review 1127710
- Monroe, I., Processes that can be embedded in Brownian motion. Ann. Probab. 6, pp. 42-56, 1978. Math. Review 0455113
- O'Brien, G.L., A limit theorem for sample maxima and heavy branches in Galton-Watson trees. J. Appl. Prob. 17, pp. 539-545, 1980. Math. Review 0568964
- Pakes, A., Extreme order statistics on Galton-Watson trees. Metrika 47, pp. 95-117, 1998. Math. Review 1622136
- Peters, R.T. and de Vilder, R.G., Testing the continuous semimartingale hypothesis for the S&P 500. J. Business and Economic Stat. 24, pp. 444-453, 2006. Math. Review number not available.
- Revuz, D. and Yor, M., Continuous Martingales and Brownian Motion, 3rd Edition. Vol. 293 of Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences). Springer-Verlag, Berlin, 1999. Math. Review 1725357
- Rolls, D.A. and Jones, O.D., Testing for continuous local martingales using the crossing tree. Australian & New Zealand J. Stat. 53, pp. 79-107, 2011. Math. Review number not available.
- Vasudev, R., Essays on time series: Time change and applications to testing, estimation and inference in continuous time models. Ph.D., Dept. Economics, Rice University, 2007.
- Wald, A. and Wolfowitz, J., On a test whether two samples are from the same population. Ann. Math. Stat. 11, 147-162, 1940. Math. Review 0002083

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