Stochastic process

High school (ages 12+)
Mathematics & Numbers

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Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/stochastic-process

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the distinguishing feature?Incorporates randomness into the description of system evolution over time
2. What is the foundational concepts?Brownian motion, Poisson processes, Markov chains, martingales
3. Why do stochastic processes involve randomness?Because the future of the system isn’t fixed even if we know its present. Randomness means we can only talk about the chances of different future states. This uncertainty makes stochastic processes useful for real‑world problems.
4. How do stochastic processes help in finance?In finance, stochastic processes are used to price options, like the Black‑Scholes model. They also help manage risk and guide algorithmic trading. They let traders understand how prices might move over time.

Stochastic Calculus: A branch of mathematics that deals with stochastic processes, extending traditional calculus.
Markov Property: The future state of a process depends only on the present state, not on past states.
Brownian Motion: A continuous-time stochastic process that models random movement, like particles in a fluid.