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I. Karatzas and S. E. Shrve, “Brownian Motion and Stochastic Calculus of Graduate Text in Mathematics,” 2nd Edition, Springer-Verlag, Berlin, 1991.

has been cited by the following article:

• TITLE: Semimartingale Property and Its Connections to Arbitrage

  AUTHORS: Sallieu Kabay Samura, Junjun Mao, Dengbao Yao

  KEYWORDS: Bichteler-Dellaccherie Theorem; Doob-Meyer Decomposition; Semi-Martingales; Arbitrage; Komlos Lemma

  JOURNAL NAME: Journal of Mathematical Finance, Vol.3 No.2, May 24, 2013

  ABSTRACT: In this paper, we prove the celebrated Bichteler-Dellaccherie Theorem which states that the class of stochastic processes X allowing for a useful integration theory consists precisely of those processes which can be written in the form X = X0 + M + A, where M0 = A0 = 0, M is a local martingale, and A is of finite variation process. We obtain this decomposition rather direct form an elementary discrete-time Doob-Meyer decomposition. By moving to convex combination we obtain a direct continuous time decomposition, which then yield the desired decomposition. We also obtain a characterization of semi-martingales in terms of a variant no free lunch with vanishing risk.