Abstract
Systems of stochastic differential equations, for which the Riemannian manifold generated by a diffusion matrix has zero curvature, are considered in this article. The method for approximate evaluation of characteristics of the solution of the systems of stochastic differential equations is proposed. This method is based on the representation of the probability density function through the functional integral. To compute functional integrals we use the expansion of action with respect to a classical trajectory, for which the action takes an extreme value. The classical trajectory is found as the solution of the multidimensional Euler – Lagrange equation.
Highlights
= αn ( x,t)dt j =1 gnj ( x, t )dw j (t), с начальным условием x(t0 ) = x0
for which the Riemannian manifold generated by a diffusion matrix has
This method is based on the representation of the probability density function
Summary
Для уравнений (5), при l = μ = n, Rμlδn = 0. Перейдем к методу вычисления функциональных интегралов вида (4), (7). Далее для вычисления интеграла можно использовать разложение действия S относительно классической траектории y кл : S [. Где интегрирование выполняется по траекториям x = δy , удовлетворяющим условиям = x (t0) 0= , x (t) 0, Для вычисления интеграла (11) используем разложение. Е. = u(t0 ) 0= ,u(t) 0, λj – собственные значения. Ассоциированной с оператором Λfree , λj – собственные значения задачи Штурма – Лиувилля, ассоциированной с оператором Λ. Находим приближенные значения функций y1кл (τ), y2кл (τ), t0 ≤ τ ≤ t, решая уравнения (16) с помощью метода сеток для решения нелинейных граничных задач [16].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
