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We propose a method to exactly generate Brownian paths $x_c(t)$ that areconstrained to return to the origin at some future time $t_f$, with a givenfixed area $A_f = \int_0^{t_f}dt\, x_c(t)$ under their trajectory. We derive anexact effective Langevin equation with an effective force that accounts for theconstraint. In addition, we develop the corresponding approach fordiscrete-time random walks, with arbitrary jump distributions including L\'evyflights, for which we obtain an effective jump distribution that encodes theconstraint. Finally, we generalise our method to other types of dynamicalconstraints such as a fixed occupation time on the positive axis$T_f=\int_0^{t_f}dt\, \Theta\left[x_c(t)\right]$ or a fixed generalisedquadratic area $\mathcal{A}_f=\int_0^{t_f}dt \,x_c^2(t)$.

Generating stochastic trajectories with global dynamical constraints