Numerical simulation for a bounded process. Is slight deviation a "normal" fact?

Question

Suppose I have to numerically simulate a process $\{y_t\}$ such that $y_t\geq0$ $\forall t\in\mathbb{N}$, with $t$ denoting time-step.

Let's suppose I use MonteCarlo with $\mathscr{N}$ simulation trajectories. Could it occur that sometimes, when running simulation, some of these $\mathscr{N}$ trajectories slightly goes beyond $0$ hence violating the condition of non-negativity of the process?
I mean: should I take this fact as an alert around the incorrectness of my simulation code or is it allowed that numerical simulation can (just "sometimes") give you some trajectories (out of the total $\mathscr{N}$) that slightly deviate from the non-negativity condition?

Answer 1

Without further information, if you know (via proof or definition) that your process cannot take on negative values for all possible values in your domain, then there's an error in your code. The alternative is that you've overlooked something in your analysis.