The stochastic wave equations driven by fractional and colored noises

被引：0
作者：
Dan Tang
Yong Jin Wang
机构：
[1] Nankai University,School of Mathematical Sciences and LPMC
[2] Nankai University,School of Mathematical Sciences and School of Business
来源：
Acta Mathematica Sinica, English Series | 2010年 / 26卷
关键词：
fractional spatial colored noise; process-valued solution; stochastic wave equations; 60H15; 35R60; 35P10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We investigate a wave equation in the plane with an additive noise which is fractional in time and has a non-degenerate spatial covariance. The equation is shown to admit a process-valued solution. Also we give a continuity modulus of the solution, and the Hölder continuity is presented.
引用
收藏
页码：1055 / 1070
页数：15
相关论文
共 14 条
  • [1] Bo L.(2008)Explosive solutions of stochastic wave equations with damping on ℝ J. Diff. Eq. 244 170-187
  • [2] Tang D.(2005)The stochastic wave equation driven by fractional Brownian noise and temporality correlated smooth noise Stoch. Dyn. 5 45-64
  • [3] Wang Y.(2002)Stochastic wave equations with polynomial nonlinearity Ann. Appl. Probab. 12 361-381
  • [4] Caithamer P.(1988)Random non-linear wave equations: smoothness of the solutions Probab. Th. Rel. Fields 79 469-508
  • [5] Chow P. L.(1999)Extending martingale measure stochastic integral with applications to homogeneous SPDEs Electron. J. Probab. 4 1-29
  • [6] Carmona R.(1998)The stochastic wave equation in two spatial dimensions Ann. Probab. 26 187-212
  • [7] Nualart D.(1999)A stochastic wave equations in two spatial dimensions: smoothness of the law Ann. Probab. 27 803-844
  • [8] Dalang R.(1997)Long-time existence for the wave equation with a noise term Ann. Probab. 25 133-151
  • [9] Dalang R.(1991)The Cauchy problem for the wave equation with distribution date: an elementary approach Amer. Math. Monthly 98 401-410
  • [10] Frangos N. E.(undefined)undefined undefined undefined undefined-undefined
12