The paper presents a vector Markov process, $P(x,t)$, which form the components of the vector $y$. The Markov process satisfies the $(n+1)$-dimensional Fokker--Planck equation partial whose solution under certain initial and boundary conditions of this presentation and the domain of the nonlinear analysis. Specifically we examine the initial and boundary conditions for the aforementioned equation, whose form \[ \frac{\partial P(y;t)}{dt}+\sum_{k=0}^{N}\frac\partial{\partial{y_k}}\Bigg\{\Bigg[K_k(y,t)-\frac12\sum_{l=0}^{N}\frac{\partial}{\partial{y_l}}{K_{lk}}(y,t)\Bigg]P(y,t)\Bigg\}=0 \] where the coefficients of intensity given by the following formulas \[ K_k(y,t)=\lim_{\triangle t\to0}\frac{E\langle\triangle y_k|y\rangle}{\triangle t}, \quad k_{lk}(y,t)=\lim_{\triangle t\to0}\frac{E\langle\triangle y_l|\triangle y_k\rangle}{\triangle t} \] and $E\langle\cdot|y\rangle$ is the mathematical expectation of the final variable for a given $y$.