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Stochastic Methods


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(r,s)-Fold Trimmed Mean Filters »

Short the samples in the window and omit r first samples and s last samples  full text »  

Bayes's Rule »

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Brownian Bridge »

The Brownian Bridge is used to generate new samples between two known samples of a Brownian motion path.  full text »  

Brownian motion: integrating »

Integrating Brownian motion.  full text »  

Brownian motion: some properties »

Properties of Brownian motion (also known as the Wiener process).  full text »  

Brownian motion: transform invariants »

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Characteristic function »

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Conditional distribution »

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Correlation coefficient »

Correlation coefficient  full text »  

Expected value »

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Independent random variables »

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Ito's formula »

Ito formula.  full text »  

Ito's lemma »

Ito's Lemma provides a derivative chain rule for stochastic functions. It gives the relationship between a stochastic process and a function of that stochastic process. A well known application in finance. When defining the returns of stock with a stochastic process, Ito's lemma is used to change the returns into stock prices.  full text »  

Ito's lemma: Z=ln(S) »

Ito's lemma.  full text »  

Jointly Normal Distribution density function »

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Mean - Variance and r-moment about the mean »

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Mean Square Estimation of r.v's »

Mean Square Estimation of r.v's  full text »  

Numerical SDE Integration: Euler Maruyama »

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Numerical SDE Integration: Milstein »

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Orthogonal r.v.'s »

Orthogonal r.v.'s  full text »  

Properties of the stochastic integral »

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