The Infinitesimal Generator

Why This Concept Matters

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Intuition Before Formalism

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Formal Definition

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Key Properties

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Connections to Other Concepts

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• Scale Function
• Speed Measure
• Invariant Density
• The Stationary Fokker–Planck Equation
• Ergodicity & Mean Reversion
• Hitting Times
• The Local Martingale ξ(Xₜ) − t
• Occupation Time & Local Time
• The Unbiased Density Estimator
• The Strong Markov Property
• Regeneration & Renewal-Reward
• Itô's Formula & Tanaka's Formula
• Optional Stopping
• Convergence Theorems & Inequalities

Worked Examples

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Further Reading

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