8 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…
Conservativeness of time changed processes and Liouville property for Schrödinger operators
Yuichi Shiozawa, Masayoshi Takeda
We establish a criterion for the Liouville property for Schrödinger operators via the conservativeness of time changed processes. Using this criterion, we obtain necessary and suff…
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…
Volume growth, big jump, and essential spectrum for regular Dirichlet forms
Yuichi Shiozawa
We establish an upper bound of the bottom of the essential spectrum for the generator associated with a regular Dirichlet form in terms of the rates of the volume growth/decay and…
Berry-Esseen bounds for large-time asymptotics of one-dimensional diffusion processes via Malliavin-Stein method
Seiichiro Kusuoka, Yuichi Shiozawa
We consider solutions of stochastic differential equations which diverge to infinity as the time parameter goes to infinity. If the coefficients converge as the spacial variable go…
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…
Berry-Esseen bound for the Brownian motions on hyperbolic spaces
Yuichi Shiozawa
We obtain the uniform convergence rate for the Gaussian fluctuation of the radial part of the Brownian motion on a hyperbolic space. We also show that this result is sharp if the d…