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. Independent onset, persistence, and detection delay
For tolerance ϵ≥0 and a window of W consecutive updates, let TW contain every candidate starting time for which the required measurements are available. Eligibility is determined without reference to declaration time. Define
Pt(ϵ,W)=1{min0≤j<Wδt+j>ϵ},
tΔ(ϵ,W)=inf{t∈TW:Pt(ϵ,W)=1}.
(2.4)
This locates the first observed qualifying window in the eligible record. When both event times are observed, their difference isExact original notation
{P}_{t}(ϵ,W)=1{{min}_{0\le j<W}{\delta }_{t+j}>ϵ},Related builds
Sources & provenance
{P}_{t}(ϵ,W)=1{{min}_{0\le j<W}{\delta }_{t+j}>ϵ},
{P}_{t}(ϵ,W)=1{{min}_{0\le j<W}{\delta }_{t+j}>ϵ},
{P}_{t}(ϵ,W)=1{{min}_{0\le j<W}{\delta }_{t+j}>ϵ},
{P}_{t}(ϵ,W)=1{{min}_{0\le j<W}{\delta }_{t+j}>ϵ},