Stochastic Integral

In this Chapter we construct the stochastic integral and show the seminal It-Formula.

Throughout, \((\Omega, \mathcal F, P)\) denotes a probability space with a filtration \(\mathbb{F}\) satisfying the usual conditions. Furthermore, unless otherwise specified, the processes are continuous.

• Doob-Meyer Decomposition
• Stochastic Integral
• Quadratic Variations - Semi-Martingales
• Itô's Formula