The propagation of cosmic rays through the heliosphere has been solved for more than half a century by stochastic methods based on Ito’s lemma. This work presents the estimation of statistical error of solution of Fokker–Planck equation by the 1D backward in time stochastic differential equations method. The error dependence on simulation statistics and energy is presented for different combinations of input parameters. The 1% precision criterion in mean value units of intensity standard deviation is defined as a function of solar wind velocity and diffusion coefficient value.

The propagation of cosmic rays through the heliosphere is solved for more than half a century by stochastic methods based on Ito's lemma. This work presents the estimation of statistical error of solution of Fokker-Planck equation by 1D forward stochastic differential equations method. The error dependence on simulation statistics and energy is presented for different combinations of input parameters. The 1% precision criterium in intensities and 1% criterium in standard deviation are defined as a function of solar wind velocity and diffusion coefficient value.

For comprehensive global modeling of cosmic rays modulation in the heliosphere, it is essential to have a sound transport theory, and reliable numerical schemes with appropriate boundary conditions. For the description of the solar modulation process, and the propagation of the particles inside the heliosphere, Parkers transport equation is widely used. The correct and precise solution of this equation also must take into consideration errors. That's why the presented work particularly focused on the estimation of the errors of the SOLARPROP model, based on the input parameters range, and statistical errors for these numerical solutions of 2D Parkers equation by stochastic differential equation method to suggest the safe simulation strategy for spectra evaluation at 1 AU. *** 27th European Cosmic RaySymposium -ECRS *** *** 25-29 July 2022 *** *** Nijmegen, the Netherlands *** * Speaker

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