Convergence of Nelson fiffusions |
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Authors: | Gianfausto Dell'Antonio Andrea Posilicano |
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Institution: | (1) Dipartimento di Matematica, Università di Roma I, I-00185 Roma, Italy;(2) S.I.S.S.A., I-34014 Trieste, Italy |
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Abstract: | Let t,
t
n
,n1, be solutions of Schrödinger equations with potentials form-bounded by –1/2 and initial data inH
1(
d
). LetP, P
n
,n1, be the probability measures on the path space =C(+,
d
) given by the corresponding Nelson diffusions. We show that if {
t
n
}
n1 converges to t inH
1(
d
), uniformly int over compact intervals, then converges to in total variation t0. Moreover, if the potentials are in the Kato classK
d
, we show that the above result follows fromH
1-convergence of initial data, andK
d
-convergence of potentials. |
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Keywords: | |
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