---
title: Stochastic Processes
description: Stochastic processes are collections of random variables representing the evolution of a system over time. Learners will understand how to model and analyze systems governed by probabilistic laws, including random walks, Poisson processes, and continuous-time systems.
category: mathematics
subcategory: probability-theory
difficulty: beginner, intermediate, advanced
url: /subject/stochastic-processes
---

# Stochastic Processes

Stochastic processes are collections of random variables representing the evolution of a system over time. Learners will understand how to model and analyze systems governed by probabilistic laws, including random walks, Poisson processes, and continuous-time systems.

## Available Resources

2 Books • 2 Courses • 2 Websites

## Courses

### 1. Discrete Stochastic Processes (MIT 6.262)

**Author:** Robert Gallager

Probabilistic systems evolving through random changes: Poisson processes, finite-state and countable Markov chains, renewal processes, random walks and martingales. 25 lecture videos, Gallager's open textbook, and problem sets and exams with solutions build the intuition to model systems in engineering, operations research and finance.

**Difficulty:** Advanced | **Price:** Free

**Link:** https://ocw.mit.edu/courses/6-262-discrete-stochastic-processes-spring-2011/

**Tags:** stochastic-processes, markov-chains, poisson-processes, renewal-theory, random-walks, martingales

### 2. An Intuitive Introduction to Probability

**Author:** Karl Schmedders

University of Zurich course taught by Karl Schmedders that builds probability from everyday examples: basic rules, conditional probability, applications, discrete random variables, and the normal distribution. Learners finish able to compute and interpret probabilities in practical decisions.

**Difficulty:** Beginner | **Language:** English | **Price:** Free

**Link:** https://www.coursera.org/learn/introductiontoprobability

**Tags:** probability, conditional-probability, discrete-random-variables, normal-distribution

## Websites

### 1. probabilitycourse.com

ProbabilityCourse.com is an online learning resource that provides a structured probability course with clear explanations, worked examples, and practice problems covering topics from basics to advanced theory.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://probabilitycourse.com

**Tags:** websites, technology-computer-science, data-science--ai

### 2. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

## Books

### 1. Introduction to Stochastic Processes

**Author:** Gregory F. Lawler

A compact graduate-level textbook covering Markov chains in discrete and continuous time, optimal stopping, martingales, renewal processes, reversible chains, Brownian motion and stochastic integration. Readers learn to model random systems and compute hitting probabilities, stationary distributions and expected waiting times.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/0412995115?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, probability-theory

### 2. Stochastic Processes

**Author:** Sheldon M. Ross

A classic graduate text built around problems and intuitive proofs, covering the Poisson process, renewal theory, Markov chains, martingales, random walks and Brownian motion. Readers learn to analyse queueing, reliability and other applied probability models using renewal and martingale arguments.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/0471099422?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, probability-theory

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