A Note on the Convergence of Integral Functionals of Diffusion Processes. An Application to Strong Convergence
Friedrich Liese, Wolfgang M. Schmidt · Mathematische Nachrichten · 1993
Abstract For a diffusion type process dXt = dWi + a(t, X)dt and a sequence (fn) of nonnegative functions necessary and sufficient conditions to the fn are established which guarantee the a.s. convergence of fn(Xt)dt to zero. This result is applied to derive simple necessary and sufficient conditions for the strong convergence of distributions of diffusion processes formulated in terms of the corresponding drift functions.