Definition
Stochastic Process
Let $(\Omega, \mathcal{F}, \mathbb{P})$ be a probability space (Definition~Probability Space) and let $T \subseteq [0, \infty)$.
A stochastic process indexed by $T$ is a collection $\{X_t\}_{t \in T}$ of random variables (Definition~Random Variable) on $\Omega$.
For each fixed $\omega \in \Omega$, the map $t \mapsto X_t(\omega)$ is called a sample path (or trajectory) of the process.
Depends on
Dependency Graph
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nbbb6ebd1["Probability Space"]
n3eb4aae1["Random Variable"]
nccabff62["Stochastic Process"]:::current
ne6452d7c["Filtration and Adapted Process"]
n72af8021["Standard Brownian Motion"]
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click nbbb6ebd1 "../objects/bbb6ebd1.html" "_self"
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click n72af8021 "../objects/72af8021.html" "_self"