A problem of frictional contact between an elastic beam and a moving foundation and the resulting wear of the beam is considered. The process is assumed to be quasistatic, the contact is modeled with normal compliance, and the wear is described by the Archard law. Existence and uniqueness of the weak solution for the problem is proved using the theory of strongly monotone operators and the Cauc...

— This paper reviews and extends some recent results on the multivariate fractional Brownian motion (mfBm) and its increment process. A characterization of the mfBm through its covariance function is obtained. Similarly, the correlation and spectral analyses of the increments are investigated. On the other hand we show that (almost) all mfBm’s may be reached as the limit of partial sums of (sup...

Article history: Received 27 July 2010 Accepted after revision 22 November 2010 Available online 24 December 2010 Presented by Marc Yor We consider the problem of a particle subject to Brownian motion in a 2D circular domain with reflecting boundaries except for an absorbing gate. An exact solution for the mean first escape time is given for a gate of any size. Also obtained is the exact probab...