A multiparameter Garsia-Rodemich-Rumsey inequality and some applications

Abstract

We extend the classical Garsia-Rodemich-Rumsey inequality to the multiparameter situation. The new inequality is applied to obtain some joint Hölder continuity along the rectangles for fractional Brownian fields $W(t,x)$ and for the solution $u(t,y)$ of stochastic heat equation with additive white noise.

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