Random Walk & Brownian Motion Simulator
Simulate and visualize 1D random walks and Brownian motion paths with empirical distributions. Explore probability and stochastic processes through interactive plots.
Formula (1D Random Walk): \( S_n = \sum_{i=1}^n X_i, \; X_i \in \{-1, 1\} \)
Brownian Motion: \( B(t) \sim \mathcal{N}(0, t) \)
For Brownian Motion, this represents time units
Simulation Results
Statistics
About Random Walks and Brownian Motion
A random walk is a mathematical object that describes a path consisting of successive random steps. The 1D random walk shown here takes steps of ±1 with equal probability.
Brownian motion is the continuous-time analog of the random walk, where the position changes according to a normal distribution with variance proportional to time.
These concepts are fundamental in probability theory, physics, finance, and many other fields.