Alòs, Elisa; Bonaccorsi, Stefano Stability for stochastic partial differential equations with Dirichlet white-noise boundary conditions. (English) Zbl 1052.60046 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5, No. 4, 465-481 (2002). The authors study a stochastic partial differential equation with boundary noise: \[ d_tu(t,x)={\partial^2\over \partial x^2}u(t,x)dt+ \sum_{j=1}^n\left[ b_j(x){\partial\over \partial x}u(t,x)+F_j(t,x,u(t,x))\right]dW^j_t, \]\[ u(t,0)={\dot V}_t,\qquad u(0,x)=u_0(x), \] where \(W^1,\dots,W^n,V\) are independent real Wiener processes. The solution is understood in a mild form, involving anticipating (Skorokhod) stochastic integrals. The authors [Ann. Inst. Henri Poincaré, Probab. Stat. 38, 125–154 (2002; Zbl 0998.60065)] have shown that under some regularity assumptions on \(b_j, F_j\) a unique solution exists. In the present paper, the existence of a unique invariant measure (on an appropriate function space) and the exponential mean-square stability are proved. Reviewer: Tomasz Bojdecki (Warszawa) Cited in 10 Documents MSC: 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35R60 PDEs with randomness, stochastic partial differential equations 35B35 Stability in context of PDEs Keywords:stochastic partial differential equations in bounded domain; boundary noise; invariant measure; exponential stability Citations:Zbl 0998.60065 PDFBibTeX XMLCite \textit{E. Alòs} and \textit{S. Bonaccorsi}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5, No. 4, 465--481 (2002; Zbl 1052.60046) Full Text: DOI References: [1] Alòs E., Probab. Statist. 38 pp 125– (2002) [2] Alós E., Probab. Statist. 36 pp 181– (2000) [3] DOI: 10.1007/s00245-001-0020-z · Zbl 0995.60056 · doi:10.1007/s00245-001-0020-z [4] Maslowski B., Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22 pp 55– (1995) [5] DOI: 10.1214/aop/1019160111 · Zbl 1044.60052 · doi:10.1214/aop/1019160111 [6] DOI: 10.1214/aop/1176988495 · Zbl 0834.60067 · doi:10.1214/aop/1176988495 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.