Browsing by Author "Iyer, Sarvesh Ravichandran"

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    Elliptic Harnack Inequality, Conformal Walk Dimension and Martingale Problem for Geometric Stable Processes
    (Indian Statistical Institute, Bangalore, 2024-07) Iyer, Sarvesh Ravichandran
    Recently, Murugan and Kajino introduced the notion of conformal walk dimension as a bridge between parabolic and elliptic Harnack inequalities. They showed that a symmetric diffusion process satisfies the elliptic Harnack inequality if and only if its conformal walk dimension equals 2, raising the question of whether a similar characterization holds for jump processes. Using the geometric stable process, we provide a counterexample: it satisfies the elliptic Harnack inequality but has infinite conformal walk dimension. Additionally, we establish the existence and uniqueness of solutions to the martingale problem associated with geometric stable processes.