Schedule-at-a-Glance

59 PRIMA 2013 Abstractsformula estimating the Hausdorff dimensions of the temperedcompact random invariant sets and investigate theexistence and the Hausdorff dimensions of random attractorsfor a stochastic wave equation with noisy damping.Data fusion based on evidence theoryYanyan HeFlorida State University, USAyhe2@math.fsu.eduData fusion techniques integrate data from multiplesources (such as sensors, institutions, and etc.), and thecombined information can help to reach more accurateand more specific inference. In this presentation, evidencetheory based combination approaches are introduced tocombine distinct sources of uncertain information. Theuncertainty in each source of information is representedby a belief function individually, which are then combinedto produce a single belief function representing informationfrom all the sources. The approaches are illustratedwith examples.The generalized Itô-Wentzell formula for Itô’sprocess and the stochastic first integralElena KarachanskayaPaciŕc National University, Russiachalykh@mail.khstu.ruWe present the Generalized Itô-Wentzell formula, whichis the generalization of Itô-Wentzell formula for a multidementionalItô’s process with the Wiener and the Poissonperturbations.This result allowed to set equations for the stochastic firstintegrals of a stochastic differential equations system.An explicit cross entropy scheme for mixturesXiang ZhouCity University of Hong Kong, Hong Kong, Chinaxiang.zhou@cityu.edu.hkThe key issue in importance sampling is the choice of thealternative sampling distribution, which is often chosenfrom the exponential tilt family of the underlying distribution.However, when the problem exhibits certain kindof nonconvexity, it is very likely that a single exponentialchange of measure will never attain asymptotic optimalityand may lead to erroneous estimates. In this paper weintroduce an explicit iterative scheme which combines thetraditional cross-entropy method and the EM algorithmto find an efficient alternative sampling distribution inthe form of mixtures. We also study the applications ofthis scheme to option price estimation.Asymptotic analysis for tipping points problemsJielin ZhuUniversity of British Columbia, Canadajielinzhu@math.ubc.caA tipping point, observed as a rapid change in climateor ecology, can be induced by a slowly varying controlparameter of a saddle-node bifurcation. The position ofthe tipping point can be significantly changed by smallnoise or periodic terms. A local multiple scaling methodis used to describe the behaviour of the system based onthe relation of the drifting rate, noise and frequency of theperiodic terms. A one-dimensional canonical slowly varyingsystem with a saddle-node bifurcation is analysed, tofind out the effect of the noise or the frequency of the periodicterms separately. We also show results for a globalenergy balance model in climate dynamics.