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• W3118906916 abstract "We study a stochastic Schrödinger equation with a quadratic nonlinearity and a space-time fractional perturbation, in space dimension <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=d less-than-or-equal-to 3> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>dleq 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. When the Hurst index is large enough, we prove local well-posedness of the problem using classical arguments. However, for a small Hurst index, even the interpretation of the equation needs some care. In this case, a renormalization procedure must come into the picture, leading to a Wick-type interpretation of the model. Our fixed-point argument then involves some specific regularization properties of the Schrödinger group, which allows us to cope with the strong irregularity of the solution." @default.
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• W3118906916 date "2021-03-30" @default.
• W3118906916 modified "2023-09-30" @default.
• W3118906916 title "A nonlinear Schrödinger equation with fractional noise" @default.
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• W3118906916 doi "https://doi.org/10.1090/tran/8368" @default.
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