Read the equation
The minimum discrepancy across the next W observations must exceed ε for the indicator to equal one. This requires every observation in the window to clear the threshold, rather than merely its average. The window beginning at t can only be confirmed once its final observation is available.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| P_t | Persistence indicator |
| epsilon | Tolerance |
| W | Number of consecutive observations; m in the earlier version |
| delta | Chosen discrepancy series |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
A finite successful window demonstrates persistence over that observed horizon, not irreversibility for all future time.
Original context
Read the surrounding source passage
2.3 Divergence and finite persistence
A measurable version of persistent discrepancy is:
Ptϵ,m=1min0≤j<mδt+j>ϵ.
The tolerance ϵ and duration m are measurement choices to be fixed before confirmatory analysis. They are not discovered by selecting whichever values make the hypothesis appear successful. For a binary or exact symbolic reference, exact equality may be meaningful. For real-valued noisy measurements, tolerance and uncertainty are essential.
The candidate post-declaration event time is:
τ=inf{t>tD:Ptϵ,m=1}.Exact original notation
{P}_{t}\left(ϵ,m\right)=1\left\{{min}_{0\le j<m}{\delta }_{t+j}>ϵ\right\}.Related builds
Sources & provenance
{P}_{t}\left(ϵ,m\right)=1\left\{{min}_{0\le j<m}{\delta }_{t+j}>ϵ\right\}.
{P}_{t}\left(ϵ,m\right)=1\left\{{min}_{0\le j<m}{\delta }_{t+j}>ϵ\right\}.
{P}_{t}\left(ϵ,m\right)=1\left\{{min}_{0\le j<m}{\delta }_{t+j}>ϵ\right\}.
{P}_{t}\left(ϵ,m\right)=1\left\{{min}_{0\le j<m}{\delta }_{t+j}>ϵ\right\}.