The problem of stability and destability in the mean square of the trivial solution of the stochastic functional differential equations systems with Poisson switchings and infinite aftereffect is investigated in the critical case.
[1] Bellman R., Cook K. Differential-difference equations. - M.: Mir, 1967. - 548 p.
[2] Gikhman I.I., Skorokhod A.V. Stochastic differential equations. - K.: Nauk. Dumka, 1969. - 354 p.
[3] Gikhman I.I., Kadyrova I.I. Some results of the study of stochastic differential equations // In the book: Theory of random processes. Vol. 1. - K.: Nauk. Dumka, 1973. - P. 51-68.
[4] Gikhman I.I., Skorokhod A.V. Stochastic differential equations and their application. - K.: Nauk. dumka, 1982. - 567 p.
[5] Dech G. Guide to the practical application of the Laplace transform and the $z$-transform. - M.: Nauka, 1969. - 367 p.
[6] Slyusarchuk V.E., Yasinsky V.K. Stability of solutions of linear stochastic functional-differential equations in the critical case. - Manuscript dep. in VINITI. - 31.03.1977. - N 1236-77 DEP.
[7] Yurchenko I.V., Yasynska L.I., Yasynskyi V.K. Methods of stochastic modeling of systems. - Chernivtsi: Publishing house "Prut", 2002. - 416 p.
[8] Yasinskaya L.I. Stability of linear functional-differential systems with discontinuous trajectories in the critical case. - Manuscript dep. in VINITI. - 30.06.1982. - N 3667-82 DEP.
[9] Sverdan M.L., Tsarkov E.F., Yasinsky V.K. Stability in stochastic modeling of complex dynamic systems.— Snyatyn: Nad Prutom, 1996.- 448 p.
[10] Yasinsky I.V., Yasinsky V.K. Lectures on the theory of stochastic modeling: Part 4. Stochastic dynamic systems with infinite aftereffect. - Chernivtsi: Green Bukovina, 2000. - 160 p.
[11] Azbelev N.V., Rakhmatulina L.F. Functional differential equations // Differential equations. - 1978. - 24, N 5. - P. 771-797.
[12] Yasinsky V.K., Antonyuk S.V. Behavior of the second moment of solutions of stochastic differential-functional equations with Poisson perturbations // Scientific Bulletin of Chernivtsi University. Mathematics. - 2003. - Issue 160. - P. 111-117.
[13] Yasinskaya L.I., Antonyuk S.V. Stability in mean square of linear singular stochastic differential-functional equations with unbounded aftereffect // 2nd International Conference "Aplimat" (Bratislava, February 5-7, 2003).— Bratislava, 2003. - P.719-724.
[14] Yasinsky V.K., Antonyuk S.V. Stability in mean square of solutions of stochastic differential-functional equations with all prehistory // 2nd International Conference "Aplimat" (Bratislava, February 5-7, 2003).- Bratislava, 2003.- P.725-732.
- ACS Style
- Antonyuk , S.V.; Yurchenko , I.V.; Yasinsky, V.K. Behavior of the second moment of solutions of stochastic functional-differential dynamical systems with discontinuous trajectories in the critical case. Bukovinian Mathematical Journal. 2018, 1
- AMA Style
- Antonyuk SV, Yurchenko IV, Yasinsky VK. Behavior of the second moment of solutions of stochastic functional-differential dynamical systems with discontinuous trajectories in the critical case. Bukovinian Mathematical Journal. 2018; 1(191).
- Chicago/Turabian Style
- Svitlana Volodymyrivna Antonyuk , Igor Valeriyovych Yurchenko , Volodymyr Kyrylovych Yasinsky. 2018. "Behavior of the second moment of solutions of stochastic functional-differential dynamical systems with discontinuous trajectories in the critical case". Bukovinian Mathematical Journal. 1 no. 191.