Tag: Diffusion Equation
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Probability Density Functions for Random Walk
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in MathematicsIf Xt is a random walk that starts from 0 at t=0, Xt~N(μt,σ2t). Its probability density is given by For a pure Brownian motion (which is a continuous RW), μ = 0 and σ = 1. This PDF satisfies the diffusion equation. For a random walk that starts elsewhere, its probability density is given by…
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Converting the Black-Scholes Equation to the Diffusion Equation
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in MathematicsThis post discusses three transformations that convert the Black-Scholes Equation to the Diffusion Equation. Black-Scholes Equation: Diffusion Equation: Note: In the images below, tau (τ) is written as l.