Abstract:
The multidimensional exponential Levy equations are used to describe many stochastic phenomena such as market fluctuations. Unfortunately in practice an exact solution does not exist for these equations. This motivates us to propose a numerical solution for n-dimensional exponential Levy equations by block pulse functions. We compute the jump integral of each block pulse function and present a Poisson operational matrix. Then we reduce our equation to a linear lower triangular system by constant, Wiener and Poisson operational matrices. Finally using the forward substitution method, we obtain an approximate answer with the convergence rate of O(h). Moreover, we illustrate the accuracy of the proposed method with a 95% confidence interval by some numerical examples.
Machine summary:
This motivates us to propose a numerical solution for n-dimensional exponential Levy equations by block pulse functions.
We compute the jump integral of each block pulse function and present a Poisson operational matrix.
[10] applied BPF for an m-dimensional linear stochastic Itô–Volterra integral equation and pre- sented the approximate solution with the convergence rate ��(ℎ).
We propose a Poisson operational matrix for the jump integral of each BPF and convert our problem to a linear lower triangular system by operational matrices and then solve it by the forward substitution method.
Hosting by IA University of Arak Press that the dynamic of the stock price process is modeled by the multidimensional exponential Levy equation, as follows: ௧ ௧ ௧(View the image of this page) The current study proceeds as follows: In section 2, we summarize some basic features of BPFs. In Section 3, we review the operational matrix [8] and the stochastic one [10].
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