Brownian motion and stochastic calculus

Continuous-time processes with continuous paths or independent increments: Kolmogorov's continuity theorem, Blumenthal-type zero–one laws, Markov property for independent-increment processes, quadratic variation, the Itô integral and Itô's formula, stochastic differential equations, the Ornstein–Uhlenbeck process, and Fokker–Planck equations for diffusions.

• Blumenthal zero–one law
• Fokker–Planck equation
• Kolmogorov continuity theorem
• Markov property of processes with independent increments
• Quadratic variation of Brownian motion
• Itô integral
• Itô's formula
• Ornstein–Uhlenbeck process

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