Self-Exciting Random Evolutions (SEREs) and their Applications (Version 2)
Bibliographic record
Abstract
This paper is devoted to the study of a new class of random evolutions (RE), so-called self-exciting random evolutions (SEREs), and their applications. We also introduce a new random process $x(t)$ such that it is based on a superposition of a Markov chain $x_n$ and a Hawkes process $N(t),$ i.e., $x(t):=x_{N(t)}.$ We call this process self-walking imbedded semi-Hawkes process (Swish Process or SwishP). Then the self-exciting REs (SEREs) can be constructed in similar way as, e.g., semi-Markov REs, but instead of semi-Markov process $x(t)$ we have SwishP. We give classifications and examples of self-exciting REs (SEREs). Then we consider two limit theorems for SEREs such as averaging (Theorem 1) and diffusion approximation (Theorem 2). Applications of SEREs are devoted to the so-called self-exciting traffic/transport process and self-exciting summation on a Markov chain, which are examples of continuous and discrete SERE. From these processes we can construct many other self-exciting processes, e.g., such as impulse traffic/transport process, self-exciting risk process, general compound Hawkes process for a stock price, etc. We present averaged and diffusion approximation of self-exciting processes. The novelty of the paper associated with new models, such as $x(t)$ and SERE, and also new features of SEREs and their many applications, namely, self-exciting and clustering effects.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".