## Stochastic Processes, Indistinguishability and Modifications

I start these notes on stochastic calculus with the definition of a continuous time stochastic process. Very simply, a stochastic process is a collection of random variables $latex {\{X_t\}_{t\ge 0}}&fg=000000$ defined on a probability space $latex {(\Omega,\mathcal{F},{\mathbb P})}&fg=000000$. That is, for each time $latex {t\ge 0}&fg=000000$, $latex {\omega\mapsto X_t(\omega)}&fg=000000$ is a measurable function from $latex {\Omega}&fg=000000$ to the real numbers.