Stability in Total Variation of Diffusion Processes with Jumps

Studies the stability in total variation norm of the diffusion process with jumps under conditions of Lipschitz and linear growth by the method of coupling. Using the theory of integral transformation a coupling of the processes is constructed. By the IT O^ formula the successful coupling is proved. The invariant probability measure is then proved to exist. The coupling inequality stability in total variation for this kind of processes is established under some conditions.