Source-pinned research
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ProbabilityTheory.locally_of_ae
Mathematical statement
If the filtration satisfies the usual conditions, then a property of the paths of a process that holds almost surely holds locally.
Source project: Brownian motion
Person-level attribution pending.
ProbabilityTheory.maximal_ineq_countable
Mathematical statement
Doob's maximal inequality for a countable index set.
Source project: Brownian motion
Person-level attribution pending.
ProbabilityTheory.maximal_ineq_finset
Project documentation
Auxiliary lemma for maximal_ineq_countable where the index set is a Finset.
Source project: Brownian motion
Person-level attribution pending.
ProbabilityTheory.measure_biUnion_altSet_le
Mathematical statement
The union of the alternation events over all finite subsets of a countable set of times below t has measure at most K / ((b - a) * m).
Source project: Brownian motion
Person-level attribution pending.
ProbabilityTheory.measure_infiniteAlt
Mathematical statement
Almost surely, there is no infinite family of alternations of X from below a to above b at times in a countable set T below t.
Source project: Brownian motion
Person-level attribution pending.
ProbabilityTheory.measureReal_altSet_le
Mathematical statement
Quantitative alternation bound: the probability of m alternations along any finite F ⊆ Iic t is at most K / m with K independent of F and m.
Source project: Brownian motion
Person-level attribution pending.