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The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a new time discretisation of these functionals corresponding to a chosen partition of the time interval and show that the convergence rate of discretisation is proportional with the square of the mesh of the partition.
The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a class of discretization schemes of thes
The detailed construction of the general solution of a second order non-homogenous linear operatordifference equation is presented. The wide applicability of such an equation as well as the usefulness of its resolutive formula is shown by studying so
We study a full discretization scheme for the stochastic linear heat equation begin{equation*}begin{cases}partial_t langlePsirangle = Delta langlePsirangle +dot{B}, , quad tin [0,1], xin mathbb{R}, langlePsirangle_0=0, ,end{cases}end{equation*} when
This paper investigates sufficient conditions for a Feynman-Kac functional up to an exit time to be the generalized viscosity solution of a Dirichlet problem. The key ingredient is to find out the continuity of exit operator under Skorokhod topology,
We demonstrate, both theoretically and experimentally, the concept of non-linear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of non-linearity.