TY  - BOOK
AU  - Iyer,Sarvesh Ravichandran
TI  - Elliptic Harnack inequality, conformal walk dimension and Martingale problem for geometric stable processes
U1  - 519 23rd
PY  - 2024///
CY  - Bengaluru
PB  - Indian Statistical Institute
KW  - Jump Processes
KW  - Harnack Inequalities
KW  - Martingale Problem
KW  - Geometric Stable Process
N1  - Thesis (Ph.D.) - Indian Statistical Institute, 2024; Includes bibliography; Elliptic Harnack inequality and geometric stable processes -- The conformal walk dimension of geometric stable processes -- The Martingale Problem -- Future work; Guided by Prof. Siva Athreya
N2  - 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
UR  - https://dspace.isical.ac.in/xmlui/handle/10263/7487
ER  -