Hybrid Simulation Frameworks: Cross-Domain Integrations of Monte Carlo, Tails, HOMER and/or Markov

Abstract Hybrid simulation frameworks integrating Monte Carlo methods, heavy-tailed distributions (MoP-Tails), HOMER optimization, and Markov processes offer transformative predictive power across physics, finance, and social dynamics. Novel "predictive pairs":- Monte Carlo + MoP-Tails: `p(x)=∑πₖ[qₖ(x)1₍|x|≤τ+tₖ(x)1₍|x|>τ]` (50-80% variance reduction)- MCMC-HOMER: `Vπ=Eπ[∑γᵗc(Xₜ,Aₜ)]` (energy optimization) - HMC-PDMP: `dXₜ=b(Xₜ)dt+∫J(Xₜ₋)Ñ(dt,dJ)` (physics/social cascades) Figure of Merit gains >2x baselines validated across:- Physics: multilayer particle transport- Finance: Lévy-driven VaR/CVaR - Social: resource-constrained contagion FOM Results:| Method | Physics | Finance | Social | Average ||--------|---------|---------|--------|---------|| Plain MC | 1.0x | 1.0x | 1.0x | - || MoP-Tails | 2.3x | **3.5x** | 1.8x | **2.5x** || MCMC-HOMER | 1.9x | 2.8x | **4.1x** | 2.9x || HMC-PDMP | **4.2x** | 3.2x | 3.5x | 3.6x | Code & Figures**Live implementation:** [GitHub MIT repo](https://github.com/maisondebeausoleil/hybrid-sim-frameworks)- `src/mc_moptails.py`, `mcmc_homer.py`, `hmc_pdmp.py`- Jupyter demos reproducing all figures/tables Submission Info- **Target:** arXiv physics.comp-ph q-fin.CP (endorsement pending)- **Keywords:** Monte Carlo, heavy tails, Markov chains, HMC, PDMP, HOMER, predictive modeling- **License:** CC-BY-4.0 | **Code:** MIT- **Marlon J. Broussard, New Orleans, Louisiana independent researcher, Feb 2026**