A multiparameter Garsia-Rodemich-Rumsey inequality and some applications

作者：Hu Yaozhong; Le Khoa^*

来源：Stochastic Processes and Their Applications, 2013, 123(9): 3359-3377.

DOI：10.1016/j.spa.2013.04.019

• Joint Holder continuity
• Garsia-Rodemich-Rumsey inequality
• Sample path property
• Gaussian processes
• Fractional Brownian fields
• Stochastic heat equations with additive noises

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

• 出版日期2013-9