Milstein Approximation for Advection-Diffusion Equations Driven by Multiplicative Noncontinuous Martingale Noises

In this paper, the strong approximation of a stochastic partial differential equation, whose differential operator is of advection-diffusion type and which is driven by a multiplicative, infinite dimensional, càdlàg, square integrable martingale, is presented. A finite dimensional projection of the infinite dimensional equation, for example a Galerkin projection, with nonequidistant time stepping is used. Error estimates for the discretized equation are derived inL 2 and almost sure senses. Besides space and time discretizations, noise approximations are also provided, where the Milstein double stochastic integral is approximated in such a way that the overall complexity is not increased compared to an Euler-Maruyama approximation. Finally, simulations complete the pape

Erwerbsorientierungen von Frauen und Einstellungen zu Erwerbstätigkeit und Familie

In East and West Germany women’s labour participation differs despite extensively harmonised institutional parameters since Reunification. In West Germany the number of working women rose in recent years; In East Germany women’s employment rate fell slightly while still remaining on a rather high level. These regional distinctions can be explained by the different employment patterns in the GDR and former FRG. In addition the varying financial household situations and different supply with child care facilities play a major role.

Multilevel Monte Carlo method for parabolic stochastic partial differential equations

We analyze the convergence and complexity of multilevel Monte Carlo discretizations of a class of abstract stochastic, parabolic equations driven by square integrable martingales. We show under low regularity assumptions on the solution that the judicious combination of low order Galerkin discretizations in space and an Euler-Maruyama discretization in time yields mean square convergence of order one in space and of order1/2 in time to the expected value of the mild solution. The complexity of the multilevel estimator is shown to scale log-linearly with respect to the corresponding work to generate a single path of the solution on the finest mesh, resp. of the corresponding deterministic parabolic problem on the finest mes

Erwerbsorientierungen von Frauen und Einstellungen zu Erwerbstätigkeit und Familie

Für Deutschland zeigen sich trotz inzwischen weitestgehend einheitlicher institutioneller Rahmenbedingungen nach wie vor deutliche Unterschiede in der Erwerbsbeteiligung von ost- und westdeutschen Frauen. Die Zahl der erwerbstätigen Frauen ist in den letzten Jahren in den alten Bundesländern gestiegen; in den neuen Ländern ist sie leicht gesunken, bewegt sich aber dennoch auf hohem Niveau. Diese Differenzen lassen sich erklären durch die unterschiedlichen Erwerbsmuster, die bei der Wiedervereinigung aufeinander trafen, aber auch durch unterschiedliche ökonomische Gegebenheiten in den Haushalten und dem regional und qualitativ unterschiedlichen Angebot an Kinderbetreuungseinrichtungen