Technical Forum • Re: Breakthrough in the theory of stochastic differential equations and their simulation

I simulated four SDEs and saved their paths at time T1 (these were Xk with K=4) and then I continued the simulation to a later time T2 and from the paths at time T2, I found the value of sum of four SDE joint simulation paths and this was variable to be conditionally predicted and I called it Y. The problem to solve is to fiund the conditional density of sum \(Y\,=\,X_1(T_2)\,+\,X_2(T_2)\,+X_3(T_2)\,+X_4(T_2)\)  given the arbitrarily chosen values of \(X1(T_1), X2(T_1), X3(T_1) \,\text{and}\,\,