PreprintarXiv licencearXiv
Complexity of flows with interactions and stochastic analysis
Abstract
We study stochastic flows with interaction through an infinite-dimensional semigroup approach. By means of a kernel lifting procedure, we represent the solution to measure-valued stochastic equation as a Hilbert-valued Markov process. We identify its generator, construct the associated Markov semigroup, and establish a dense range condition using measure polynomial functionals. The results provide a framework for the analysis of stability of stochastic equations with interaction.
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BibTeX
@misc{shi2026complexity,
title = {{Complexity of flows with interactions and stochastic analysis}},
author = {Yifan Shi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06924},
eprint = {2610.06924},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06924},
}
RIS
TY - UNPB
TI - Complexity of flows with interactions and stochastic analysis
AU - Yifan Shi
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.06924
UR - https://arxiv.org/abs/2610.06924
AB - We study stochastic flows with interaction through an infinite-dimensional semigroup approach. By means of a kernel lifting procedure, we represent the solution to measure-valued stochastic equation as a Hilbert-valued Markov process. We identify its generator, construct the associated Markov semigroup, and establish a dense range condition using measure polynomial functionals. The results provide a framework for the analysis of stability of stochastic equations with interaction.
ER -