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Effect of Volatility and Drift on Random Walks

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number of steps
volatility (resample)
maximum absolute drift(resample)
auto zoom
off
on
drift
This Demonstration generates 10 sample paths of Brownian motion with values of drift governed by a user-defined maximum absolute value. The user can vary the number of steps and volatility of the random walk. A random walk is a mathematical model for the motion of particles in suspension in a fluid. The volatility represents the temperature of the fluid and drift represents an external force applied to the particles, such as an electric field. Drift values are the same for the
x
and
y
axes, resulting in drifting directions {1,1} and {-1,1}.
The sampling occurs dynamically with the addition of new steps, i.e. if the user goes back and forth in the number of steps, the simulation will generate a different path each time.
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