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Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the development and application of the Fourier method to the numerical solution of Ito stochastic differential equations. Fourier series are widely used in various fields of applied mathematics and physics. However, the method of Fourier series as applied to the numerical solution of stochastic differential equation...

Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the comparative analysis of the efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations under the method of approximating multiple Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. Using the mul...

Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractA strongly converging method of order 2.5 for Ito stochastic differential equations with multidimensional nonadditive noise based on the unified Taylor–Stratonovich expansion is proposed. The focus is on the approaches and methods of mean square approximation of iterated Stratonovich stochastic integrals of multiplicities 1–5 the numerical ...

Phan, Tuan Anh Tian, Jianjun Paul
Published in
Mathematical biosciences and engineering : MBE

The complexity of oncolytic virotherapy arises from many factors. In this study, we incorporate environmental noise and stochastic effects to our basic deterministic model and propose a stochastic model for viral therapy in terms of Ito stochastic differential equations. We conduct a detailed analysis of the model using boundary methods. We find tw...

Komori, Yoshio Cohen, David Burrage, Kevin

Komori, Yoshio Cohen, David Burrage, Kevin

Boucekkine, Raouf Zou, Benteng

This note studies the stochastic stability of the standard AK growth model under uncertain output technology. Capital accumulation follows a stochastic linear homogenous differential equation. It's shown that exponential balanced paths, which characterize optimal trajectories in the absence of uncertainty, are not robust to uncertainty. Precisely, ...

Batou, Anas Soize, Christian

The research addressed here concerns the generation of seismic accelerograms compatible with a given response spectrum and other associated properties. The time sampling of the stochastic accelerogram yields a time series represented by a random vector in high dimension. The probability density function (pdf) of this random vector is constructed us...

Guilleminot, Johann Soize, Christian

This paper is concerned with the construction of a new class of generalized nonparametric probabilistic models for matrix-valued non-Gaussian random fields which may take its values in some subset of the set of real symmetric positive-definite matrices presenting sparsity and invariance with respect to given orthogonal transformations. Within the c...