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dc.contributor.author | Gliklikh, Yu. E. | |
dc.contributor.author | Mashkov, E. Yu. | |
dc.contributor.author | Гликлих, Ю. Е. | |
dc.contributor.author | Машков, Е. Ю. | |
dc.date.accessioned | 2015-09-28T09:04:34Z | |
dc.date.available | 2015-09-28T09:04:34Z | |
dc.date.issued | 2013 | |
dc.identifier.citation | Gliklikh, Yu. E. Stochastic leontieff type equations and mean derivatives of stochastic processes / Yu. E. Gliklikh, E. Yu. Mashkov // Вестник ЮУрГУ. Серия Математическое моделирование и программирование.- 2013.- Т. 6. № 2.- С. 25-39.- Библиогр.: с. 37 (14 назв.) | ru_RU |
dc.identifier.issn | 2071-0216 | |
dc.identifier.uri | http://dspace.susu.ac.ru/xmlui/handle/0001.74/5291 | |
dc.description | Yu.E. Gliklikh, Voronezh State University, Voronezh, Russian Federation, yeg@math.vsu.ru, E.Yu. Mashkov, Kursk State University, Kursk, Russian Federation, mashkovevgen@yandex.ru. | ru_RU |
dc.description.abstract | We understand the Leontieff type stochastic differential equations as a special sort of Ito stochastic differential equations, in which the left-hand side contains a degenerate constant linear operator and the right-hand side has a non-degenerate constant linear operator. In the right-hand side there is also a summand with a term depending only on time. Its physical meaning is the incoming signal into the device described by the operators mentioned above. In the papers by A.L. Shestakov and G.A. Sviridyuk the dynamical distortion of signals is described by such equations. Transition to stochastic differential equations arise where it is necessary to take into account the interference (noise). Note that the investigation of solutions of such equations requires the use of derivatives of the incoming signal and the noise of any order. In this paper for differentiation of noise we apply the machinery of the so-called Nelson's mean derivatives of stochastic processes. This allows us to avoid using the machinery of the theory of generalized functions. We present a brief introduction to the theory of mean derivatives, investigate the transformation of the equations to canonical form and find formulae for solutions in terms of Nelson's mean derivatives of Wiener process. | ru_RU |
dc.language.iso | other | ru_RU |
dc.publisher | Издательский центр ЮУрГУ | ru_RU |
dc.relation.isformatof | Вестник ЮУрГУ. Серия Математическое моделирование и программирование | ru_RU |
dc.relation.isformatof | Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya Matematicheskoe modelirovanie i programmirovanie | ru_RU |
dc.relation.isformatof | Bulletin of SUSU | ru_RU |
dc.relation.ispartofseries | Математическое моделирование и программирование;Том 6 | |
dc.subject | mean derivative | ru_RU |
dc.subject | current velocity | ru_RU |
dc.subject | Wiener process | ru_RU |
dc.subject | Leontieff type equation | ru_RU |
dc.subject | производная в среднем | ru_RU |
dc.subject | текущая скорость | ru_RU |
dc.subject | винеровский процесс | ru_RU |
dc.subject | уравнение леонтьевского типа | ru_RU |
dc.subject | УДК 517.9 | ru_RU |
dc.subject | УДК 517.216.2 | ru_RU |
dc.subject | ГРНТИ 27.43 | ru_RU |
dc.title | Stochastic leontieff type equations and mean derivatives of stochastic processes | ru_RU |
dc.title.alternative | Стохастические уравнения леонтьевского типа и производные в среднем случайных процессов | ru_RU |
dc.type | Article | ru_RU |