2025/07/31 by Choi, Jaehyung
#Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Information Theory (cs.IT) #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2507.23646
We explore the information geometry of Lévy processes. As a starting point, we derive the α-divergence between two Lévy processes. Subsequently, the Fisher information matrix and the α-connection associated with the geometry of Lévy processes are computed from the α-divergence. In addition, we discuss statistical applications of this information geometry. As illustrative examples, we investigate the differential-geometric structures of various Lévy processes relevant to financial modeling, including tempered stable processes, the CGMY model, and variance gamma processes.