What is a stochastic process?

A stochastic process is a mathematical object defined as a collection of random variables. It represents the evolution of some system of values over time. Unlike a deterministic system (where if you know the start, you know the end), a stochastic system has multiple possible futures, each with its own probability.

Why does the same math work for stock markets and physics?

Brownian Motion (the random motion of particles in a fluid) and the Black-Scholes model (used to price options) share the same underlying math: the Wiener Process. In both cases, we assume that changes are random, independent, and follow a normal distribution. While markets aren't actually perfectly normal (they have 'fat tails'), the approximation is useful enough to build global financial infrastructure.

What is a Poisson process?

A Poisson process models events that happen independently at a constant average rate. It's used to model things like server requests, calls to a help desk, or radioactive decay. The key property is 'memorylessness'—the time you wait for the next event doesn't depend on how long you've already been waiting.

How does math unify these domains?

Universality. In complex systems, the details of the individual components often matter less than the global structure. Whether it's molecules, traders, or neurons, if they interact in specific ways, the system as a whole will inevitably follow specific probability distributions (like the Power Law or the Central Limit Theorem).

What are the limitations of these models?

Real data has fat tails (jump-diffusion needed), systems get stuck in traps (path dependence), and humans learn (non-stationarity). The math is a map, not the territory.

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One Math, Four Domains: How Stochastic Processes Unify Finance, Systems, Physics, and Biology

March 26, 2026·1 min read·by Vache Sarkissian

↻Updated June 3, 2026

✓Reviewed March 29, 2026

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Written by Claude (Opus 4.6) — Vache prompted, reviewed, and published. The data and benchmarks are real; the prose is AI-generated.

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About the Author

Vache Sarkissian

Building research infrastructure and products at the intersection of knowledge systems and machine learning. Creator of Linesheet Pro, vault-search, and the vachsark learning engine.

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One Math, Four Domains: How Stochastic Processes Unify Finance, Systems, Physics, and Biology

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