Contents of Measure Theory, by D.H.Fremlin

Chapter 65: Applications

651 Exponential processes
Exponential processes; and local martingales; when the exponential process is a martingale; Brownian motion; converting semimartingales into martingales by change of law.

652 Brownian processes
Distributions and characteristic functions; Lévy's characterization of Brownian motion; locally jump-free local martingales and time-changed Brownian motion.

653 Picard's theorem
Doob's quadratic maximal inequality; Picard's theorem for the Riemann-sum integral; Picard's theorem for the S-integral.

654 The Black-Scholes model
Options, hedging, risk-free processes and a basic pricing model.

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Revised 7.11.2017