Stochastic processes
Systems whose individual steps are unpredictable but whose distribution is describable.
A stochastic process is a sequence of random steps. The individual steps can't be predicted, but the distribution of outcomes often can. Random walks (each step random, but the walk has predictable variance), Poisson processes (events happening at random with known average rate), and Markov chains (where each step depends only on the current state) are all examples.
The practical implication: many things that look hopelessly chaotic actually have a structure once you describe them stochastically. You can't predict the next stock price tick. You can describe the distribution of where prices will be in a month.
For operators, this matters when:
- Forecasting under uncertainty (the right unit is a distribution, not a number)
- Detecting genuine signal in noisy time series
- Pricing options, insurance, or any asymmetric payoff
Examples in the wild
Customer support inbound volumes are roughly Poisson-distributed at most companies. Knowing the distribution lets you staff for the 95th percentile, not the average.
Stock prices are roughly random walks with drift. The drift is the slow upward trend; the walk is the daily noise. Most active investing is fighting the noise.
Traffic delays at any specific commute time are stochastic. Building 20% buffer in your departure time handles most days; building 5x buffer handles the rare bad days.
Stochastic processes is one of the mental models we apply through real cases inside the Pareto MBA — a part-time program for professionals who want to think clearly about business.