Exact spatio-temporal moduli of continuity, small-ball estimates, and iterated logarithm laws are established for nonlinear parabolic SPDEs and extended to the open KPZ equation on the unit interval.
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Fourier dimension of the graph of fBM with H ≥ 1/2 is a.s. 1, established via a new combinatorial integration by parts formula combined with Faà di Bruno's formula and strong local nondeterminism.
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On the spatio-temporal increments of nonlinear parabolic SPDEs and the open KPZ equation
Exact spatio-temporal moduli of continuity, small-ball estimates, and iterated logarithm laws are established for nonlinear parabolic SPDEs and extended to the open KPZ equation on the unit interval.
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Fourier dimension of the graph of fractional Brownian motion with $H \ge 1/2$
Fourier dimension of the graph of fBM with H ≥ 1/2 is a.s. 1, established via a new combinatorial integration by parts formula combined with Faà di Bruno's formula and strong local nondeterminism.