Almost sure asymptotic stability and convergence of stochastic Theta methods applied to systems of linear SDEs in
Bibliographic record
Abstract
Abstract Almost sure asymptotic stability of trivial solution and almost sure convergence of stochastic Theta methods applied to bilinear systems of ordinary stochastic differential equations (SDEs) of Itô-type in are proven. For this purpose, we prove and exploit a convergence theorem for non-negative semi-martingale decompositions, and verify a practical criteria based on the uniform boundedness of nonrandom eigenvalues related to certain matrix systems in any dimension d . We do not assume commutativity or simultaneous diagonalizability of drift and diffusion parts as many other authors, neither we restrict our analysis and applicability to only 2D or 3D cases nor to uniform step sizes (since the problem of adequate stochastic test equations cannot be solved within non-anticipative Itô calculus). However, an example of 2D diagonal-noised systems illustrates our approach. The discrete time systems of stochastic Theta methods are driven by L 2 -martingales (i.e. martingale differences, not necessarily Gaussian) and can be interpreted as nonautonomous discretizations (e.g. with variable step sizes or dependence on time).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".