2012.15201
Random Time Dynamical Systems I: General Structures
Yuri Kondratiev, José Luís da Silva
correctmedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Proposition 3.1 derives v(t,x) ∼ t^{γ−1}Q(t)/(α|v|Γ(γ)) via the subordination formula v(t,x)=∫ u(τ,x)G_t(τ)dτ with u(τ,x)=e^{−α|v|τ}, then applies Lemma 2.10 on A(t,z)=∫ e^{−zτ}G_t(τ)dτ. The candidate solution follows the same steps, explicitly identifying v(t,x)=A(t,α|v|) and invoking the same asymptotic to obtain the identical constant. The candidate also notes the v=0 edge case, which the paper implicitly avoids by using |v| in the denominator. Overall, both are correct and essentially identical in method.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The audited proposition is correct, and the argument is tight: it cleanly applies the subordination formula and a standard asymptotic lemma for inverse subordinators. The contribution is mainly illustrative within a broader programmatic paper on random time changes in dynamical systems. Minor clarifications (explicitly excluding v=0 in the statement, notational disambiguation) would improve accessibility without altering the substance.