Информационная система "Конференции"

Тезисы докладов

Стохастическое моделирование и методы Монте-Карло

Consider the mixed problem for the evolutionary equation % begin{equation}label{eq:diff_eq} V'(t)=A(t)V(t) + B(t)V(t); V(t_0)=V_0; V(t)in Z_t, t>0, end{equation} % where $V(t)$ is the required vector function with values in a Banach space $L$, $A(t)$ and $B(t)$ are linear and continuous operators accordingly. Set of boundary conditions $Z_t$ is considered as an affine subspace in $L$. Set $widetilde{Z}_t$ is directing one for $Z_t$. The generalized solution to the problem (ref{eq:diff_eq}) is the solution to the integral equation % begin{equation}label{eq:integr_eq} V(t) = u(t,t_0)V_0 + int_{t_0}^t widetilde{u}(t,s) B(s)V(s)ds, end{equation} % where $u(t,s): Z_s rightarrow Z_t$ is an evolutionary operator for a nonperturbed problem $(B(t)equiv0)$, $widetilde{u}(t,s): widetilde{Z}_s rightarrow widetilde{Z}_t$ is an operator, associated with $u(t,s)$, $B(t): Z_t rightarrow widetilde{Z}_t$ (it does not break boundary conditions). It is shown in this work that if $B(t)$ is the affine operator, the solution to the equation (ref{eq:integr_eq}) has probabilistic representation.

Примечание. Тезисы докладов публикуются в авторской редакции

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