Abstract
We study the existence, uniqueness and Hölder regularity of the solution to a stochastic semilinear equation arising from 1-dimensional integro-differential scalar conservation laws. The equation is driven by double-parameter fractional noises. In addition, the existence and moment estimate are also obtained for the density of the law of such a solution.
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Liu, J., Yan, L. On a semilinear stochastic partial differential equation with double-parameter fractional noises. Sci. China Math. 57, 855–872 (2014). https://doi.org/10.1007/s11425-013-4703-0
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DOI: https://doi.org/10.1007/s11425-013-4703-0
Keywords
- stochastic partial differential equations
- double-parameter fractional noises
- Hölder regularity
- density of the law
- Malliavin calculus