Numerical solution of a matrix integral equation arising in Markov Modulated Lévy processes
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Markov-modulated Lévy processes lead to matrix integral equations of the kind A_0 + A_1X+A_2 X^2+A_3(X)=0 where A_0, A_1, A_2 are given matrix coefficients, while A_3(X) is a nonlinear function, expressed in terms of integrals involving the exponential of the matrix X itself. In this paper we propose some numerical methods for the solution of this class of matrix equations, perform a theoretical convergence analysis and show the effectiveness of the new methods by means of a wide numerical experimentation.
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