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The cosmic rays modulation inside the heliosphere is well described by atransport equation introduced by Parker in 1965. To solve this equation severalapproaches were followed in the past. Recently the Monte Carlo approach becomeswidely used in force of his advantages with respect to other numerical methods.In the Monte Carlo approach, the transport equation is associated to a fullyequivalent set of Stochastic Differential Equations. This set is used todescribe the stochastic path of a quasi-particle from a source, e.g., theinterstellar medium, to a specific target, e.g., a detector at Earth. In thiswork, we present both the Forward-in-Time and Backward-in-Time Monte Carlosolutions. We present an implementation of both algorithms in the framework ofHelMod Code showing that the difference between the two approach is below 5\%that can be quoted as the systematic uncertain of the Method itself.

Cosmic Rays Propagation with HelMod: Difference between forward-in-time and backward-in-time approaches