Brownian motion is the first and most studied example of a stochastic process. By this term, we mean the temporal evolution of a system that does not obey purely deterministic laws. The main characteristic of a stochastic process, as opposed to deterministic systems, is that the trajectory of the system is not determined solely by the initial conditions (It is true that even a deterministic system, for example certain ordinary differential equations, can have a non-unique solution given the initial condition. For example, the differential equation \(dx/dt=x^{1/3}\) with the initial condition \(x(0)=0\) has two solutions: \(x(t)=0\) and \(x(t)=(2t/3)^{3/2}\) . The non-uniqueness is due to the failure of the Lipschitz condition at \(x=0\) .). In the case of stochastic processes, different trajectories characterized by a probability distribution evolve from the same initial condition.