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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)

We investigate in this paper the numerical performances of quadratic functional quantization and their applications to Finance. We emphasize the rôle played by the so-called product quantizers and the Karhunen-Lò eve expansion of Gaussian processes. Numerical experiments are carried out on two classical pricing problems : Asian options in a Black-Scholes… (More)

This paper is concerned with numerical approximations for a class of nonlinear stochastic partial differential equations : Zakai equation of nonlinear filtering problem and McKean-Vlasov type equations. The approximation scheme is based on the representation of the solutions as weighted conditional distributions. We first accurately analyse the error caused… (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)

This paper is concerned with numerical approximations for stochastic partial differential Zakai equation of nonlinear filtering problem. The approximation scheme is based on the representation of the solutions as weighted conditional distributions. We first accurately analyse the error caused by an Euler type scheme of time discretization. Sharp error… (More)