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Stochastic Convective Wave Equation in Two Space Dimension

We study the convective wave equation in two space dimension driven by spatially homogeneous Gaussian noise. The existence of the real-valued solution is proved by providing a necessary and sufficient condition of Gaussian noise source. Our approach is based on the mild solution of the convective wave equation which is constructed by Walsh's theory of martingale measures. Hölder continuity of the solution is proved by using Green's function and Kolmogorov continuity theorem.

preprint2014arXivOpen access
Sang-Hyeon ParkImbo Sim
math.PR
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Open access2 authors1 topic
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Sang-Hyeon ParkImbo Sim

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