Abstract
We consider three magnetic relativistic Schrödinger operators which correspond to the same classical symbol $\sqrt{(\xi - A(x))^2 + m^2} + V(x)$ and whose heat semigroups admit the Feynman-Kac-Itô type path integral representation $E[e^{ - S^m (x,\,t;\,X)} g(x + X(t))]$. Using these representations, we prove the convergence of these heat semigroups when the mass-parameter $m$ goes to zero. Its proof reduces to the convergence of $e^{- S^m (x,\,t;\,X)}$, which yields a limit theorem for exponentials of semimartingales as functionals of Lévy processes $X$.
Citation
Taro Murayama. "A probabilistic approach to the zero-mass limit problem for three magnetic relativistic Schrödinger heat semigroups." Tsukuba J. Math. 40 (1) 1 - 28, July 2016. https://doi.org/10.21099/tkbjm/1474747485
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