MathIsimple

Stochastic Processes

Master stochastic processes through rigorous probability theory foundations, random process analysis, and mathematical modeling

Mathematical RigorSelf-Paced LearningUniversity Level

🎯 Foundation Topics

Master essential concepts and build strong foundations for stochastic process theory

Available!
🎲
Beginner to Intermediate
Probability Theory Prerequisites
Master essential probability theory foundations: random experiments, events, probability measures, conditional probability, independence, and Bayes' theorem
12 lessons
8-12 hours

What you'll learn:

  • Random Experiments & Sample Spaces
  • Classical, Statistical & Geometric Probability
  • Conditional Probability & Bayes' Theorem
  • Independence & Product Spaces
  • Complete Probability Foundations
  • Essential Stochastic Prerequisites
Available!
🔍
Intermediate to Advanced
Stochastic Process Fundamentals
Master core concepts of stochastic processes: definitions, classification, sample functions, finite-dimensional distributions, and numerical characteristics
8 lessons
6-10 hours

What you'll learn:

  • Stochastic Process Definition & Classification
  • Parameter Sets & State Spaces
  • Sample Functions & Realizations
  • Finite-Dimensional Distributions
  • Mean Functions & Correlation Functions
  • Gaussian Processes & Special Properties
Available!
🔗
Advanced
Markov Chains
Explore discrete-time Markov processes: transition probabilities, state classifications, stationary distributions, and absorption probabilities with practical applications
10 lessons
8-12 hours

What you'll learn:

  • Markov Property & Definition
  • Transition Matrices & Chapman-Kolmogorov Equations
  • State Classification: Recurrent & Transient
  • Periodicity & Irreducibility
  • Stationary Distributions & Limiting Behavior
  • Absorption Probabilities & Gambler's Ruin
Available!
📈
Advanced
Independent Increment Processes
Master independent increment processes: definitions, properties, mean functions, covariance structures, and applications to random walks and Brownian motion
8 lessons
6-10 hours

What you'll learn:

  • Independent Increment Definition & Properties
  • Mean Function Additivity & Covariance Simplification
  • Markov Property & Statistical Characteristics
  • Random Walks & Simple Stochastic Processes
  • Connection to Poisson & Brownian Motion
  • Practical Applications & Real-World Examples
Available!
📊
Advanced
Poisson Processes
Master Poisson processes: definitions, properties, event timing, time intervals, synthesis and decomposition with practical applications to counting processes
10 lessons
8-12 hours

What you'll learn:

  • Poisson Process Definitions & Equivalence
  • Core Properties: Mean, Variance & Covariance
  • Event Timing & Time Interval Distributions
  • Conditional Distributions & Uniform Properties
  • Synthesis & Decomposition of Poisson Processes
  • Non-Homogeneous Poisson Processes & Applications
Available!
🌊
Advanced
Brownian Motion
Master Brownian motion: standard and general processes, Wiener processes, Brownian bridges, geometric Brownian motion with applications to finance and physics
12 lessons
10-14 hours

What you'll learn:

  • Standard Brownian Motion & Wiener Process
  • General Brownian Motion with Drift & Diffusion
  • Brownian Bridge Processes & Boundary Conditions
  • Geometric Brownian Motion & Financial Applications
  • Reflection Principle & First Passage Times
  • Maximum Distribution & Self-Similarity Properties

New to Stochastic Processes?

Start with "Probability Theory Prerequisites" to build a solid foundation. This comprehensive module covers random experiments, conditional probability, independence, and Bayes' theorem - essential concepts for understanding stochastic processes.

Practice Problems