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Optimal quantization has been recently revisited in multi-dimensional numerical integration (see [18]), multi-asset American option pricing (see [1]), Control Theory (see [19]) and Nonlinear Filtering Theory (see [20]). In this paper, we enlighten some numerical procedures in order to get some accurate optimal quadratic quantization of the Gaussian(More)
In this paper we study the approximation of the distribution of X t Hilbert–valued stochastic process solution of a linear parabolic stochastic partial differential equation written in an abstract form as dX t + AX t dt = Q 1/2 dW t , X 0 = x ∈ H, t ∈ [0, T ], driven by a Gaussian space time noise whose covariance operator Q is given. We assume that A −α is(More)
We investigate in this paper the numerical performances of quadratic functional quantization with some applications to Finance. We emphasize the rôle played by the so-called product quantiz-ers and the Karhunen-Lò eve expansion of Gaussian processes, in particular the Brownian motion. We show how to build some efficient functional quantizers for Brownian(More)
In this paper we investigate a discrete approximation in time and in space of a Hilbert space valued stochastic process {u(t)} t∈[0,T ] satisfying a stochastic linear evolution equation with a positive-type memory term driven by an additive Gaussian noise. The equation can be written in an abstract form as du + t 0 b(t − s)Au(s) ds dt = dW Q , t ∈ (0, T ];(More)
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