Statistical problems in Hilbert spaces. Application to filtering theory
Local solutions for stochastic Navier Stokes equations
Smooth solutions of systems of quasilinear parabolic equations
We consider in this article diagonal parabolic systems arising in the context of stochastic differential games. We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear hamiltonian seems to be the...
Systems of Bellman Equations to Stochastic Differential Games with Discount Control
We consider two dimensional diagonal elliptic systems which arise from stochastic differential games with discount control. The Hamiltonians have quadratic growth in and a special structure which has notyet been covered by regularity theory. Without smallness condition on , the existence of a regular solution is established.
Asymptotic behaviour of the time dependent Norton-Hoff law in plasticity theory and regularity
We prove -regularity for the stresses in the Prandtl-Reuss-law. The proof runs via uniform estimates for the Norton-Hoff-approximation.
-regularity results for quasilinear parabolic systems
On Bellman systems without zero order term in the context of risk sensitive differential games
Bellman systems corresponding to stochastic differential games arising from a cost functional which models risk aspects are considered. Here it leads to diagonal elliptic systems without zero order term so that no simple -estimate is available.
Smooth Solutions of systems of quasilinear parabolic equations
We consider in this article diagonal parabolic systems arising in the context of stochastic differential games. We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear Hamiltonian seems to be...
Local Solutions for Stochastic Navier Stokes Equations
In this article we consider local solutions for stochastic Navier Stokes equations, based on the approach of Von Wahl, for the deterministic case. We present several approaches of the concept, depending on the smoothness available. When smoothness is available, we can in someway reduce the stochastic equation to a deterministic one with a random parameter. In the general case, we mimic the concept of local solution for stochastic differential equations.
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