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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

Prof. Michael Roeckner, Bielefeld University and AMSS, CAS

Inviter: 李利平
Title:
Variational solutions to nonlinear stochastic differential equations in Hilbert spaces
Time & Venue:
2018.6.20 16:30-17:30 N613
Abstract:
One introduces a new variational concept of solution for the stochastic differential equation dX+A(t)Xdt+λXdt=XdW,t∈(0,T); X(0)=x in a real Hilbert space where A(t)=?φ(t), t∈(0,T), is a maximal monotone subpotential operator in H while W is a Wiener process in H on a probability space {Ω,,?}. In this new context, the solution X=X(t,x) exists for each x∈H, is unique, and depends continuously on x. This functional scheme applies to a general class of stochastic PDE not covered by the classical variational existence theory and, in particular, to stochastic variational inequalities and parabolic stochastic equations with general monotone nonlinearities with low or superfast growth to +∞.
 

 

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