Novel hemodynamic markers derived from stochastic modeling of blood pressure fluctuations and brain oxygenation reveal quantifiable links between cerebrovascular dysfunction and Alzheimer's pathology. The study used transcranial Doppler and near-infrared spectroscopy to create statistical indices of cerebral blood flow regulation in cognitively impaired and healthy older adults, finding that better vascular function correlated with larger hippocampal volumes and reduced amyloid burden on PET imaging. This work advances our understanding of the vascular hypothesis of Alzheimer's disease, which proposes that compromised brain blood flow contributes to neurodegeneration alongside traditional amyloid and tau pathology. The correlation between hemodynamic indices and established AD biomarkers suggests cerebrovascular health may serve as both an early warning system and therapeutic target. However, the cross-sectional design limits causal inferences about whether vascular dysfunction drives cognitive decline or vice versa. The hemodynamic modeling approach represents a sophisticated advance over simple blood flow measurements, potentially offering clinicians objective markers to assess brain vascular health before overt cognitive symptoms emerge. This could prove especially valuable for identifying at-risk individuals and monitoring interventions targeting cerebrovascular function in Alzheimer's prevention strategies.