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Stochastic hölder continuity of random fields governed by a system of stochastic PDEs

Journal Article


Abstract


  • This paper constructs a solvability theory for a system of stochastic partial differential equations. On account of the Kolmogorov continuity theorem, solutions are looked for in certain Hölder-type classes in which a random field is treated as a space-time function taking values in Lp-space of random variables. A modified stochastic parabolicity condition involving p is proposed to ensure the finiteness of the associated norm of the solution, which is showed to be sharp by examples. The Schauder-type estimates and the solvability theorem are proved.

Publication Date


  • 2020

Citation


  • Du, K., Liu, J., & Zhang, F. (2020). Stochastic hölder continuity of random fields governed by a system of stochastic PDEs. Annales de l'institut Henri Poincare (B) Probability and Statistics, 56(2), 1230-1250. doi:10.1214/19-AIHP1000

Scopus Eid


  • 2-s2.0-85082519589

Start Page


  • 1230

End Page


  • 1250

Volume


  • 56

Issue


  • 2

Abstract


  • This paper constructs a solvability theory for a system of stochastic partial differential equations. On account of the Kolmogorov continuity theorem, solutions are looked for in certain Hölder-type classes in which a random field is treated as a space-time function taking values in Lp-space of random variables. A modified stochastic parabolicity condition involving p is proposed to ensure the finiteness of the associated norm of the solution, which is showed to be sharp by examples. The Schauder-type estimates and the solvability theorem are proved.

Publication Date


  • 2020

Citation


  • Du, K., Liu, J., & Zhang, F. (2020). Stochastic hölder continuity of random fields governed by a system of stochastic PDEs. Annales de l'institut Henri Poincare (B) Probability and Statistics, 56(2), 1230-1250. doi:10.1214/19-AIHP1000

Scopus Eid


  • 2-s2.0-85082519589

Start Page


  • 1230

End Page


  • 1250

Volume


  • 56

Issue


  • 2