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has been cited by the following article:

• TITLE: An Upper Bound for Conditional Second Moment of the Solution of a SDE

  AUTHORS: Andriy Yurachkivsky

  KEYWORDS: Conditional Expectation; Martingale; Stochastic Equation

  JOURNAL NAME: Applied Mathematics, Vol.4 No.1, January 28, 2013

  ABSTRACT: Let be a filtration on some probability space and let denote the class of all -adapted -valued stochastic processes M such that for all t>s≥0 and the process is continuous (the conditional expectations are extended, so we do not demand that . It is shown that each is a locally square integrable martingale w. r. t. . Let X be the strong solution of the equation where , t is a continuous increasing process with -measurable values at all times, and Q is an -valued random function on , continuous in and -progressive at fixed x. Suppose also that there exists an -measurable in nonnegative random process Ψ such that, for all Then where