A Note on $\mathbb{L}_{2}$-structure of Continuous-time Bilinear Processes with Time-varying Coefficients
Bibliographic record
Abstract
This paper is concerned with the investigation of $\mathbb{L}_{2}$-structureissue of time-varying coefficients continuous-time bilinear processes ($COBL$)driven by a Brownian motion $\left(BM\right)$. Such processes are veryuseful for modeling irregular spacing non linear and non Gaussian datasets andmay be proposed to model for instance some financial returns representing highamplitude oscillations and thus make it a serious candidate for describeprocesses with time-varying degree of persistence and other complex systems.Our attention is focused however on the probabilistic structure of $COBL$processes, so, we establish necessary and sufficient conditions for theexistence of regular solutions in term of their transfer function. Expliciteformulas for the mean and covariance functions are given. As a consequence, weobserve that the second order structure is similar to a $CARMA$ processes withsome uncorrelated noise. Therefore, it is necessary to look intohigher-order cumulant in order to distinguish between $COBL$ and $CARMA$ processes.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".