Wyniki wyszukiwania - Biblioteka Nauki

1

On the convergence of the wavelet-Galerkin method for nonlinear filtering

100%

Nowak Ł. , Pasławska-Południak M. , Twardowska K.

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nr 1

93-108

EN

The aim of the paper is to examine the wavelet-Galerkin method for the solution of filtering equations. We use a wavelet biorthogonal basis with compact support for approximations of the solution. Then we compute the Zakai equation for our filtering problem and consider the implicit Euler scheme in time and the Galerkin scheme in space for the solution of the Zakai equation. We give theorems on convergence and its rate. The method is numerically much more efficient than the classical Galerkin method.

2

Numerical schemes for multivalued backward stochastic differential systems

88%

Maticiuc L. , Rotenstein E.

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tom 10

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nr 2

693-702

EN

We define approximation schemes for generalized backward stochastic differential systems, considered in the Markovian framework. More precisely, we propose a mixed approximation scheme for the following backward stochastic variational inequality: $$dY_t + F(t,X_t ,Y_t ,Z_t )dt \in \partial \phi (Y_t )dt + Z_t dW_t ,$$ where ∂φ is the subdifferential operator of a convex lower semicontinuous function φ and (X t)t∈[0;T] is the unique solution of a forward stochastic differential equation. We use an Euler type scheme for the system of decoupled forward-backward variational inequality in conjunction with Yosida approximation techniques.

3

On the convergence of the wavelet-Galerkin method for nonlinear filtering

63%

Nowak Ł. D. , Pasławska-Południak M. , Twardowska K.

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2010

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tom Vol. 20, no 1

93-108

EN

The aim of the paper is to examine the wavelet-Galerkin method for the solution of filtering equations. We use a wavelet biorthogonal basis with compact support for approximations of the solution. Then we compute the Zakai equation for our filtering problem and consider the implicit Euler scheme in time and the Galerkin scheme in space for the solution of the Zakai equation. We give theorems on convergence and its rate. The method is numerically much more efficient than the classical Galerkin method.