Yuichi Shiozawa

Finite Explosion for One-dimensional L\'evy Driven SDEs and its Application to SPDEs

We study finite-time explosion to $-\infty$ 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 $b$ is locally Lipschitz and $(L_t)_{t\ge0}$ is a pure-jump L\'evy process. We give verifiable conditions involving Osgood-type integrability under which ex...