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math.PR2025
Feynman Formula for Discrete-time Quantum Walks
Jean-Pierre Fouque, Tomoyuki Ichiba, Ka Lok Lam
We explicitly connect (discrete-time) quantum walks on Z with a four-state Markov additive process via a Feynman-type formula (2.5). Using this representation, we derive a relation…
math.PR2024
Semimartingale properties of a generalized fractional Brownian motion and its mixtures with applications in asset pricing
Tomoyuki Ichiba, Guodong Pang, Murad S. Taqqu
We study the semimartingale properties for the generalized fractional Brownian motion (GFBM) introduced by Pang and Taqqu (2019) and discuss the applications of the GFBM and its mi…