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math.PR2026
Finite Explosion for One-dimensional Lévy Driven SDEs and its Application to SPDEs
Pei-Sen Li, Yuichi Shiozawa, Jian Wang
We study finite-time explosion to for the one-dimensional stochastic differential equation \[ X_t^x=x-\int_0^t b(X_s^x)\,\dd s+L_t,\quad x\in\R, \] where is locally L…
math.PR2026
Essential spectrum for Brox-type diffusion processes
Yuichi Shiozawa, Jian Wang
This paper investigates the essential spectrum and compactness property of Markov semigroups generated by multi-dimensional Brox diffusion processes under two types of random media…