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# Questions tagged [brownian]

Brownian motion is the random motion of particles (eg atoms) that make up a gas. The math used to model Brownian motion is sometimes used in statistics to describe stochastic processes over time.

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### How is the augmented Dickey–Fuller test (ADF) table of critical values calculated?

Could you please explain in simple terms how the table of critical values for the augmented Dickey–Fuller (ADF) test is created?
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### Simulating a Brownian Excursion using a Brownian Bridge?

I would like to simulate a Brownian excursion process (a Brownian motion that is conditioned always be positive when $0 \lt t \lt 1$ to $0$ at $t=1$). Since a Brownian excursion process is a Brownian ...
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### Book on stochastic processes

What is good applied book on stochastic processes? Specifically, a book that focuses on Wiener process and Brownian motion. PS: Preferably free
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### Matlab Regenerating figures: Simulating Brownian Motion via Random Walks

I'm trying to understand the relation between discrete-time random walk process and continuous-time wiener process. I'm reading this lectures and to understand concepts and proofs I need to ...
Let's say we have geometric Brownian motion: $$dS_t = \mu S_tdt + \sigma S_tdW_t$$ Then the SDE becomes: $$S_t = S_0\exp\left(\left(\mu - \frac{\sigma^2}{2}\right)t + \sigma W_t\right)$$ Say $\mu$ ...