Local Nondeterminism and Local Times of the Stochastic Wave Equation Driven by Fractional-Colored Noise

Springer Science and Business Media LLC - Tập 28 Số 2 - Trang 1-38 - 2022
Lee, Cheuk Yin1
1Institut de mathématiques, École polytechique fédérale de Lausanne, Lausanne, Switzerland

Tóm tắt

We investigate the existence and regularity of the local times of the solution to a linear system of stochastic wave equations driven by a Gaussian noise that is fractional in time and colored in space. Using Fourier analytic methods, we establish strong local nondeterminism of the solution and the existence of jointly continuous local times. We also study the differentiability and moduli of continuity of the local times and deduce some sample path properties of the solution.

Tài liệu tham khảo

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