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Stochastic Processes Formulas

Complete mathematical reference for stochastic processes with KaTeX-rendered formulas and quick access to essential equations

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📐 Foundation Formulas

Essential mathematical formulas for stochastic process foundations

Available!
🎲
Beginner to Intermediate
Probability Theory Prerequisites
Essential probability formulas: axioms, conditional probability, Bayes' theorem, independence, and basic probability calculations
25

formulas included

Formula categories:

  • Probability Axioms & Properties
  • Conditional Probability Formulas
  • Bayes' Theorem & Applications
  • Independence & Product Rules
  • Basic Probability Calculations
Available!
🔍
Intermediate to Advanced
Stochastic Process Fundamentals
Essential formulas for stochastic process definitions, classification, numerical characteristics, and Gaussian process properties
20

formulas included

Formula categories:

  • Process Definition & Structure Formulas
  • Classification & State Space Formulas
  • Mean Functions & Autocorrelation
  • Variance & Autocovariance Functions
  • Gaussian Process Properties
  • Cross-Correlation & Joint Process Formulas
Available!
🔗
Advanced
Markov Chains
Comprehensive formulas for discrete-time Markov processes including transition probabilities, stationary distributions, absorption problems, and ergodic theory
30

formulas included

Formula categories:

  • Markov Property & Basic Definitions
  • Chapman-Kolmogorov Equations & Matrix Powers
  • State Classification & Recurrence Formulas
  • Stationary Distributions & Balance Equations
  • Absorption Probabilities & Gambler's Ruin
  • PageRank & Special Applications
Available!
📈
Advanced
Independent Increment Processes
Essential formulas for independent increment processes: mean functions, covariance structures, random walk properties, and connection to advanced processes
25

formulas included

Formula categories:

  • Independent Increment Definition & Properties
  • Mean Function Additivity & Covariance Simplification
  • Markov Property & Statistical Characteristics
  • Random Walk Formulas & Applications
  • Connection to Poisson & Brownian Motion
  • Advanced Properties & Theorems
Available!
📊
Advanced
Poisson Processes
Essential formulas for Poisson processes: increment probabilities, event timing distributions, time intervals, and synthesis/decomposition properties
28

formulas included

Formula categories:

  • 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
Essential formulas for Brownian motion: standard and general processes, Wiener processes, Brownian bridges, geometric Brownian motion
32

formulas included

Formula categories:

  • Standard Brownian Motion & Wiener Process
  • General Brownian Motion with Drift & Diffusion
  • Brownian Bridge Process & Boundary Conditions
  • Reflection Principle & First Passage Time
  • Geometric Brownian Motion & Financial Applications
  • Self-Similarity & Scaling Properties
Coming Soon
📊
Intermediate
Random Variables & Distributions
Formulas for discrete and continuous random variables, probability distributions, joint distributions, and transformations
20

formulas included

Formula categories:

  • Probability Mass & Density Functions
  • Cumulative Distribution Functions
  • Joint & Marginal Distribution Formulas
  • Transformation Techniques
  • Common Distribution Formulas
Coming Soon
🎯
Intermediate
Mathematical Expectation & Variance
Formulas for expectation, variance, covariance, correlation, moment generating functions, and numerical characteristics
18

formulas included

Formula categories:

  • Mathematical Expectation Formulas
  • Variance & Standard Deviation
  • Covariance & Correlation Formulas
  • Moment Generating Functions
  • Joint Distribution Characteristics
Coming Soon
∞
Advanced
Limit Theorems
Convergence formulas, law of large numbers, central limit theorem, and fundamental limit theorem equations
15

formulas included

Formula categories:

  • Convergence Type Definitions
  • Law of Large Numbers Formulas
  • Central Limit Theorem Equations
  • Chebyshev & Markov Inequalities
  • Characteristic Function Methods

🚀 Advanced Formulas

Advanced stochastic process theory formulas and equations

Advanced
Coming Soon
Markov Chain Formulas
Transition matrices, Chapman-Kolmogorov equations, stationary distributions, and state classification formulas
12

formulas planned

Planned categories:

  • Transition Matrix Operations
  • Chapman-Kolmogorov Equations
  • Stationary Distribution Formulas
  • State Classification Methods
Advanced
Coming Soon
Stochastic Calculus
Itô's lemma, stochastic differential equations, Brownian motion formulas, and geometric Brownian motion
15

formulas planned

Planned categories:

  • Itô's Lemma & Applications
  • Stochastic Differential Equations
  • Brownian Motion Properties
  • Geometric Brownian Motion
Advanced
Coming Soon
Martingale Theory
Martingale definitions, stopping times, optional sampling theorem, and convergence theorems
10

formulas planned

Planned categories:

  • Martingale Properties
  • Stopping Time Formulas
  • Optional Sampling Theorem
  • Convergence Results

Looking for Specific Formulas?

Start with "Stochastic Process Fundamentals" formulas for core mathematical definitions and properties. All formulas are professionally rendered with KaTeX and include detailed explanations.

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