Brownian Motion

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Brownian Motion. Chuan -Hsiang Han November 24, 2010. Symmetric Random Walk. Given ; let and , and denotes the outcome of th toss. Define the r.v. 's that for each A S.R.W. is a process such that and. Independent Increments of S.R.W. - PowerPoint PPT Presentation

Transcript of Brownian Motion

Brownian Motion

Brownian MotionChuan-Hsiang HanNovember 24, 2010Symmetric Random WalkIndependent Increments of S.R.W.Martingale Property of S.R.W.Markov Property of S.R.W.Quadratic Variation of S.R.W.Scaled S.R.W.Properties of Scaled S.R.W.Limiting (Marginal) Distribution of S.R.W.A Numerical ExampleLog-Normality as the Limit of the Binomial ModelWhat is Brownian Motion?Standard Brownian MotionsCovariance MatrixJoint Moment-Generating Function of BMAlternative Characteristics of BrownianMotion (Theorem 3.3.2)Filtration for B.M.Martingale propertyLevy's Characteristics of Brownian MotionVariations: First-Order (Total) VariationQuadratic VariationQuadratic Variation of B.M.Geometric Brownian MotionVolatility Estimation of GBMBM is a Markov process