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

• 作者: Andriy Yurachkivsky
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: CONDITIONAL EXPECTATION MARTINGALE STOCHASTIC Equation
• 年，卷（期）: 2013,（1）
• 页码范围: 135-143
• 页数: 9页
• 分类号: O1

摘要

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