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Information × Registration Number 0216U001005, 0115U000087 , R & D reports Title Analytical methods of stochastic differential equations popup.stage_title Head Baev Artem Victorovich, Registration Date 04-01-2016 Organization Donetsk National University popup.description2 Object of study - stochastic differential equations with jumps. The goal - to identify sufficient conditions for ergodicity solutions of differential equations with jumps, use and evaluation equations with jumps of small parameter at transfer coefficient to describe noisy weak signal detection conditions for sufficient differentiation probability of transition problems in the application of actuarial and financial mathematics. Methods - probabilistic methods, techniques Bensoussan A., Lions J.-L., Papanicolaou G. The methods and techniques study of differential equations of parabolic type on which the Bilateral be output estimates for the fundamental solution of a parabolic equation. With built bilateral assessments be output sufficient conditions for the existence Doblina hypothesis that will continue to prescribe the rate of convergence to ergodic distribution. As a method of proof used the approach of continuous processes corresponding Markov chains. Used modified methods and techniques developed Veretennikov AJ, Bismut JM, Stroock DW, SRS Varadhan for research hipoeliptychnosti parabolic partial differential equations, leaving sufficient conditions are found for the existence of the second order derivatives including fundamental solution for parabolic systems. The results of research implemented in the educational process in teaching academic Disciplines "Actuarial and financial calculations" masters specialty "Actuarial and financial mathematics" of the Faculty of Mathematics and Information Technologies of Donetsk National University of MES of Ukraine. Product Description popup.authors Баев Артем Викторович Болдирєва Валерія Олегівна Козаченко Юрій Васильович Козир Сергій Михайлович Петранова Марина Юріївна Сенаторов Олег Сергійович Хейлик Ярослав Сергійович popup.nrat_date 2020-04-02 Close