On the Cauchy problem for stochastic integro-differential equations with radially O-regularly varying Lévy measure (Q2045415)

The authors study the stochastic parabolic Cauchy problem \begin{gather*} du(t,x) = [ Lu(t,x) - \lambda u(t,x) + f(t,x)] dt + \int_U \Phi (t,x,z) q(dt,dz) \\ u(0,x) = g(x), \quad (t,x) \in E = [0,T] \times \mathbb{R}^d \end{gather*} for \(\lambda \geq 0\). Here \[ L \phi(x) = \int [\phi(x+) - \phi(x) - \chi_{\sigma}(y) y \nabla \phi(x)] \nu(dy), \quad \phi \in C_0^{\infty} (\mathbb{R}^d). \] They prove both existence and uniqueness of a solution by deriving a priori estimates.