Continuous Time Processes: Lebesgue-Stieljes Integral, Martingales

In this Chapter we will extend the notion of stochastic processes to the continuous time setting, that is, processes where time takes positive real values. Throughout, \((\Omega, \mathcal F, P)\) denotes a probability space. Unless otherwise specified, stochastic processes are always implicitly considered as indexed by time \(0\leq t < \infty\).

Warning

Unless otherwize specified, the letters \(q\) and \(r\) used for time means that they are rational.

• Continuous Time Processes
• Lebesgue-Stieljes Integral
• Martingales