4 papers
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…
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…
Lyapunov exponents and growth indices for fractional stochastic heat equations with space-time Lévy white noise
Yuichi Shiozawa, Jian Wang
We consider fractional stochastic heat equations with space-time Lévy white noise of the form Here, the…
Spatial asymptotic behaviors of fractional stochastic heat equations driven by additive Lévy white noise
Yuichi Shiozawa, Jian Wang
We establish explicit integral tests for spatial asymptotic behaviors of fractional stochastic heat equations driven by additive Lévy white noise. Our results indicate that fractio…