%0 Journal Article %1 mueller1997finite %A Mueller, C. %A Tribe, R. %D 1997 %J Electron. J. Probab. %K Fisher-KPP SPDE spatial_spread travelling_wave %P no. 7, 27 pp. (electronic) %R 10.1214/EJP.v2-21 %T Finite width for a random stationary interface %U http://dx.doi.org/10.1214/EJP.v2-21 %V 2 %X We study the asymptotic shape of the solution u(t,x)∈0,1 to a one-dimensional heat equation with a multiplicative white noise term. At time zero the solution is an interface, that is u(0,x) is 0 for all large positive x and u(0,x) is 1 for all large negitive x. The special form of the noise term preserves this property at all times t≥0. The main result is that, in contrast to the deterministic heat equation, the width of the interface remains stochastically bounded.

@article{mueller1997finite, abstract = { We study the asymptotic shape of the solution u(t,x)∈[0,1] to a one-dimensional heat equation with a multiplicative white noise term. At time zero the solution is an interface, that is u(0,x) is 0 for all large positive x and u(0,x) is 1 for all large negitive x. The special form of the noise term preserves this property at all times t≥0. The main result is that, in contrast to the deterministic heat equation, the width of the interface remains stochastically bounded.}, added-at = {2013-01-20T14:24:53.000+0100}, author = {Mueller, C. and Tribe, R.}, biburl = {https://www.bibsonomy.org/bibtex/23b5fd2368889157ab5a8a95155fc0941/peter.ralph}, doi = {10.1214/EJP.v2-21}, fjournal = {Electronic Journal of Probability}, interhash = {51fcff341664d230987acd51c0356839}, intrahash = {3b5fd2368889157ab5a8a95155fc0941}, issn = {1083-6489}, journal = {Electron. J. Probab.}, keywords = {Fisher-KPP SPDE spatial_spread travelling_wave}, mrclass = {60H15 (35R60)}, mrnumber = {1485116 (99g:60106)}, mrreviewer = {Richard B. Sowers}, pages = {no. 7, 27 pp. (electronic)}, timestamp = {2013-09-12T22:23:01.000+0200}, title = {Finite width for a random stationary interface}, url = {http://dx.doi.org/10.1214/EJP.v2-21}, volume = 2, year = 1997 }