Lesson plan
Increasing process
An increasing process is a stochastic process... : (X_t)_{t \in M} ...where the random variables X_t which make up the process are increasing almost surely and adapted: : 0=X_0 \leq X_{t_1} \leq \cdots . A continuous increasing process is such a process where the set M is continuous. Consider a stochastic process (\Chi_t) satisfying X_t \leq X_s a.s. for all t \leq s My question is: Does there exist a modification \breve{X} of , X which almost surely has increasing sample paths t \mapsto \breve{X}_t(\omega) ?
Article summary
An increasing process is a stochastic process... : (X_t)_{t \in M} ...where the random variables X_t which make up the process are increasing almost surely and adapted: : 0=X_0 \leq X_{t_1} \leq \cdots . A continuous increasing process is such a process where the set M is continuous. Consider a stochastic process (\Chi_t) satisfying X_t \leq X_s a.s. for all t \leq s My question is: Does there exist a modification \breve{X} of , X which almost surely has increasing sample paths t \mapsto \breve{X}_t(\omega) ?
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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