Bibliographic record
Abstract
Pardoux and Veretennikov [Ann. Probab., 29, (2001), 1061–1085], establish existence (in the Sobolev sense) and uniqueness of solutions of a Poisson equation for the differential operator of an ergodic diffusion in for which the covariance term is strictly non-degenerate and uniformly bounded. Our goal is to establish a similar solvability result, but for the complementary case of singular diffusions, in which the covariance is not necessarily of full-rank. In return for abandoning strict positive-definiteness of the covariance, we postulate second-order smoothness of the coefficients of the diffusion, and, to secure ergodicity, we postulate a “stability” condition on the eigenvalues of the symmetrized Jacobian matrix of the drift. We establish existence of solutions of the Poisson equation in the classical sense, and use this to characterize limits in a time-scales problem arising from perturbation of a stochastic differential equation by a rescaled singular diffusion; this is motivated by a stochastic averaging principle of Liptser and Stoyanov [Stochastics and Stochastics Reports, 32, (1990), 145–163].
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 | 0.000 | 0.001 |
| 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".