Unifying non-Markovian Dynamics and Agent Heterogeneity in Scalable Stochastic Networks
Abstract
Stochastic processes underpin dynamics across biology, physics, epidemiology, and finance, yet accurately simulating them remains a major challenge. Classical approaches such as the Gillespie algorithm are exact for Markovian, time-independent systems, where propensities depend only on the current state and agents of a given type are statistically identical. While efficient, this framework misses a defining feature of many real systems: heterogeneity and memory at the level of individual agents. Cells may divide or differentiate on distinct intrinsic timescales, individuals may preferentially interact with specific partners, and inter-event-time distributions can deviate strongly from the exponential. We introduce MOSAIC (Modeling of Stochastic Agents with Individual Complexity), a general and scalable framework that embeds agent-specific properties directly into the dynamics. MOSAIC unifies heterogeneous rates, dynamic interaction preferences, and both Markovian and non-Markovian waiting-time distributions within a single stochastic formalism, while retaining Gillespie-like computational cost.
Related
- Duality for Stochastic Control with non-Markovian Random Coefficients
- Convergence in Hölder norms for Markovian approximations of stochastic Volterra equations
- Berry--Esseen bounds for stochastic approximation with Markovian noise
- The Quantum Stochastic Limit for Non-Markovian Driving Processes
- Multidimensional Infinite-Horizon Markovian Backward Stochastic Differential Equations with Continuous Coefficients and Nonzero-Sum Differential Games
BibTeX
@article{pelissier2026unifying,
title = {{Unifying non-Markovian Dynamics and Agent Heterogeneity in Scalable Stochastic Networks}},
author = {Aurelien Pelissier and Miroslav Phan and Didier Le Bail and Niko Beerenwinkel and Maria Rodriguez Martinez},
journal = {Nature Communications},
year = {2026},
month = sep,
doi = {10.1038/s41467-026-69817-y},
eprint = {2609.31125},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05763067v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Unifying non-Markovian Dynamics and Agent Heterogeneity in Scalable Stochastic Networks
AU - Aurelien Pelissier
AU - Miroslav Phan
AU - Didier Le Bail
AU - Niko Beerenwinkel
AU - Maria Rodriguez Martinez
PY - 2026
DA - 2026/09/24
JO - Nature Communications
DO - 10.1038/s41467-026-69817-y
UR - https://hal.science/hal-05763067v1
AB - Stochastic processes underpin dynamics across biology, physics, epidemiology, and finance, yet accurately simulating them remains a major challenge. Classical approaches such as the Gillespie algorithm are exact for Markovian, time-independent systems, where propensities depend only on the current state and agents of a given type are statistically identical. While efficient, this framework misses a defining feature of many real systems: heterogeneity and memory at the level of individual agents. Cells may divide or differentiate on distinct intrinsic timescales, individuals may preferentially interact with specific partners, and inter-event-time distributions can deviate strongly from the exponential. We introduce MOSAIC (Modeling of Stochastic Agents with Individual Complexity), a general and scalable framework that embeds agent-specific properties directly into the dynamics. MOSAIC unifies heterogeneous rates, dynamic interaction preferences, and both Markovian and non-Markovian waiting-time distributions within a single stochastic formalism, while retaining Gillespie-like computational cost.
SN - 2041-1723
SN - 2041-1723
ER -