Shaikhet, Leonid; Caraballo, Tomás Stability of delay evolution equations with fading stochastic perturbations. (English) Zbl 1490.60191 Int. J. Control 95, No. 6, 1515-1521 (2022). MSC: 60H15 35K57 35Q30 PDFBibTeX XMLCite \textit{L. Shaikhet} and \textit{T. Caraballo}, Int. J. Control 95, No. 6, 1515--1521 (2022; Zbl 1490.60191) Full Text: DOI
Shaikhet, Leonid Behavior of solution of stochastic delay differential equation with additive fading perturbations. (English) Zbl 1453.34104 Appl. Math. Lett. 111, Article ID 106640, 9 p. (2021). MSC: 34K50 34K27 60J76 PDFBibTeX XMLCite \textit{L. Shaikhet}, Appl. Math. Lett. 111, Article ID 106640, 9 p. (2021; Zbl 1453.34104) Full Text: DOI
Shaikhet, Leonid Stability of delay differential equations with fading stochastic perturbations of the type of white noise and Poisson’s jumps. (English) Zbl 1458.34139 Discrete Contin. Dyn. Syst., Ser. B 25, No. 9, 3651-3657 (2020). Reviewer: Yong-Kui Chang (Xi’an) MSC: 34K50 34K20 34K27 PDFBibTeX XMLCite \textit{L. Shaikhet}, Discrete Contin. Dyn. Syst., Ser. B 25, No. 9, 3651--3657 (2020; Zbl 1458.34139) Full Text: DOI
Shaikhet, Leonid Stability of the zero and positive equilibria of two connected neoclassical growth models under stochastic perturbations. (English) Zbl 1508.91349 Commun. Nonlinear Sci. Numer. Simul. 68, 86-93 (2019). MSC: 91B62 91B70 34K60 PDFBibTeX XMLCite \textit{L. Shaikhet}, Commun. Nonlinear Sci. Numer. Simul. 68, 86--93 (2019; Zbl 1508.91349) Full Text: DOI
Shaikhet, Leonid Multi-condition of stability for nonlinear stochastic non-autonomous delay differential equation. (English) Zbl 1456.34078 Mod. Stoch., Theory Appl. 5, No. 3, 337-351 (2018). MSC: 34K50 34K20 60G55 37C60 PDFBibTeX XMLCite \textit{L. Shaikhet}, Mod. Stoch., Theory Appl. 5, No. 3, 337--351 (2018; Zbl 1456.34078) Full Text: DOI arXiv
Shaikhet, Leonid Efimovich About some asymptotic properties of solution of stochastic delay differential equation with a logarithmic nonlinearity. (English) Zbl 1474.34566 Funct. Differ. Equ. 24, No. 1-2, 57-67 (2017). MSC: 34K50 34K20 60H10 34K25 34K21 PDFBibTeX XMLCite \textit{L. E. Shaikhet}, Funct. Differ. Equ. 24, No. 1--2, 57--67 (2017; Zbl 1474.34566) Full Text: Link
Caraballo, Tomás; Shaikhet, Leonid Stability of delay evolution equations with stochastic perturbations. (English) Zbl 1316.60104 Commun. Pure Appl. Anal. 13, No. 5, 2095-2113 (2014). Reviewer: Ruhollah Jahanipur (Kashan) MSC: 60H15 60G52 35R60 35K35 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{L. Shaikhet}, Commun. Pure Appl. Anal. 13, No. 5, 2095--2113 (2014; Zbl 1316.60104) Full Text: DOI
Shaikhet, Leonid Stability of equilibrium points of differential equation with fractional nonlinearity and stochastic perturbations. (English) Zbl 1381.34105 Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 19, No. 6, 709-729 (2012). MSC: 34K50 34K20 PDFBibTeX XMLCite \textit{L. Shaikhet}, Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 19, No. 6, 709--729 (2012; Zbl 1381.34105) Full Text: Link
Shaikhet, L. E.; Roberts, J. A. Asymptotic stability analysis of a stochastic Volterra integro-differential equation with fading memory. (English) Zbl 1263.93196 Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 18, No. 6, 749-770 (2011). MSC: 93D20 93E03 93E15 93E25 PDFBibTeX XMLCite \textit{L. E. Shaikhet} and \textit{J. A. Roberts}, Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 18, No. 6, 749--770 (2011; Zbl 1263.93196) Full Text: Link
Shaikhet, L. Some new aspects of Lyapunov-type theorems for stochastic differential equations of neutral type. (English) Zbl 1235.34212 SIAM J. Control Optim. 48, No. 7, 4481-4499 (2010). Reviewer: Michael Scheutzow (Berlin) MSC: 34K50 34K20 34K40 34K06 PDFBibTeX XMLCite \textit{L. Shaikhet}, SIAM J. Control Optim. 48, No. 7, 4481--4499 (2010; Zbl 1235.34212) Full Text: DOI
Paternoster, Beatrice; Shaikhet, Leonid Stability of equilibrium points of fractional difference equations with stochastic perturbations. (English) Zbl 1149.39007 Adv. Difference Equ. 2008, Article ID 718408, 21 p. (2008). MSC: 39A11 39A20 93E15 37H10 PDFBibTeX XMLCite \textit{B. Paternoster} and \textit{L. Shaikhet}, Adv. Difference Equ. 2008, Article ID 718408, 21 p. (2008; Zbl 1149.39007) Full Text: DOI EuDML
Rodkina, Alexandra; Schurz, Henri; Shaikhet, Leonid Almost sure stability of some stochastic dynamical systems with memory. (English) Zbl 1148.39011 Discrete Contin. Dyn. Syst. 21, No. 2, 571-593 (2008). Reviewer: Christian Pötzsche (München) MSC: 39A11 34F05 60H10 37H10 34K50 39A12 PDFBibTeX XMLCite \textit{A. Rodkina} et al., Discrete Contin. Dyn. Syst. 21, No. 2, 571--593 (2008; Zbl 1148.39011) Full Text: DOI
Shaikhet, Leonid E.; Roberts, Jason A. Reliability of difference analogues to preserve stability properties of stochastic Volterra integro-differential equations. (English) Zbl 1133.65003 Adv. Difference Equ. 2006, Article ID 73897, 22 p. (2006). MSC: 65C30 60H20 60H35 45J05 45R05 45M10 PDFBibTeX XMLCite \textit{L. E. Shaikhet} and \textit{J. A. Roberts}, Adv. Difference Equ. 2006, Article ID 73897, 22 p. (2006; Zbl 1133.65003) Full Text: DOI EuDML
Shaikhet, Leonid General method of Lyapunov functionals construction in stability investigations of nonlinear stochastic difference equations with continuous time. (English) Zbl 1083.39010 Stoch. Dyn. 5, No. 2, 175-188 (2005). Reviewer: Alexandra Rodkina (Kingston/Jamaica) MSC: 39A11 37H10 60H25 PDFBibTeX XMLCite \textit{L. Shaikhet}, Stoch. Dyn. 5, No. 2, 175--188 (2005; Zbl 1083.39010) Full Text: DOI
Kolmanovskii, V. B.; Shaikhet, L. E. Matrix Riccati equations and stability of stochastic linear systems with nonincreasing delays. (English) Zbl 1148.93346 Funct. Differ. Equ. 4, No. 3-4, 279-293 (1997). Reviewer: Volker Wihstutz (Charlotte) MSC: 93E03 34F05 34K50 93E15 93D20 PDFBibTeX XMLCite \textit{V. B. Kolmanovskii} and \textit{L. E. Shaikhet}, Funct. Differ. Equ. 4, No. 3--4, 279--293 (1997; Zbl 1148.93346)
Kolmanovskij, V. B.; Shajkhet, L. E. Control of systems with aftereffect. Transl. from the Russian by Victor Kotov. (English) Zbl 0937.93001 Translations of Mathematical Monographs. 157. Providence, RI: American Mathematical Society (AMS). xi, 336 p. (1996). Reviewer: A.Akutowicz (Berlin) MSC: 93-02 49-02 34K35 49K25 93E20 93C23 49L20 49N10 PDFBibTeX XMLCite \textit{V. B. Kolmanovskij} and \textit{L. E. Shajkhet}, Control of systems with aftereffect. Transl. from the Russian by Victor Kotov. Providence, RI: AMS, American Mathematical Society (1996; Zbl 0937.93001)
Shaikhet, Leonid E. Stability of stochastic hereditary systems with Markov switching. (English) Zbl 0939.60049 Theory Stoch. Process. 2(18), No. 3-4, 180-184 (1996). Reviewer: Yu.V.Kozachenko (Kyïv) MSC: 60H10 60J60 PDFBibTeX XMLCite \textit{L. E. Shaikhet}, Theory Stoch. Process. 2(18), No. 3--4, 180--184 (1996; Zbl 0939.60049)
Shaikhet, Leonid E. Modern state and development perspectives of Lyapunov functionals method in the stability theory of stochastic hereditary systems. (English) Zbl 0893.60029 Theory Stoch. Process. 2(18), No. 1-2, 248-259 (1996). Reviewer: M.P.Moklyachuk (Kyïv) MSC: 60H10 93E15 34F05 PDFBibTeX XMLCite \textit{L. E. Shaikhet}, Theory Stoch. Process. 2(18), No. 1--2, 248--259 (1996; Zbl 0893.60029)
Shaikhet, L. E. Stability in probability of nonlinear stochastic systems with delay. (English. Russian original) Zbl 0843.93086 Math. Notes 57, No. 1, 103-106 (1995); translation from Mat. Zametki 57, No. 1, 142-146 (1995). Reviewer: E.Yaz (Fayetteville) MSC: 93E15 93C10 34K35 PDFBibTeX XMLCite \textit{L. E. Shaikhet}, Math. Notes 57, No. 1, 103--106 (1995; Zbl 0843.93086); translation from Mat. Zametki 57, No. 1, 142--146 (1995) Full Text: DOI
Kolmanovskij, V.; Shaikhet, L. New results in stability theory for stochastic functional differential equations (SEDEs) and their applications. (English) Zbl 0811.34062 Ladde, G. S. (ed.) et al., Dynamic systems and applications. Vol. 1. Proceedings of the 1st international conference, held at Morehouse College, Atlanta, GA, USA, May 26-29, 1993. Atlanta, GA: Dynamic Publishers, Inc. 167-171 (1994). Reviewer: M.Scheutzow (Berlin) MSC: 34K50 60H10 34K20 PDFBibTeX XMLCite \textit{V. Kolmanovskij} and \textit{L. Shaikhet}, in: Dynamic systems and applications. Vol. 1. Proceedings of the 1st international conference, held at Morehouse College, Atlanta, GA, USA, May 26-29, 1993. Atlanta, GA: Dynamic Publishers, Inc.. 167--171 (1994; Zbl 0811.34062)
Kolmanovskij, V. B.; Shaikhet, L. E. Successive approximations to the optimal control of stochastic systems with after-effect. II. (English) Zbl 0848.93064 Random Oper. Stoch. Equ. 1, No. 4, 375-392 (1993). Reviewer: M.Scheutzow (Berlin) MSC: 93E20 PDFBibTeX XMLCite \textit{V. B. Kolmanovskij} and \textit{L. E. Shaikhet}, Random Oper. Stoch. Equ. 1, No. 4, 375--392 (1993; Zbl 0848.93064) Full Text: DOI
Kolmanovskij, V. B.; Shajkhet, L. E. On a method to construct Lyapunov functionals for stochastic systems with aftereffect. (English. Russian original) Zbl 0815.34068 Differ. Equations 29, No. 11, 1657-1666 (1993); translation from Differ. Uravn. 29, No. 11, 1909-1920 (1993). Reviewer: V.Chernyatin (Szczecin) MSC: 34K50 34K20 34F05 34D20 93E03 93E15 PDFBibTeX XMLCite \textit{V. B. Kolmanovskij} and \textit{L. E. Shajkhet}, Differ. Equations 29, No. 11, 1909--1920 (1993; Zbl 0815.34068); translation from Differ. Uravn. 29, No. 11, 1909--1920 (1993)
Kolmanovskij, V. B.; Shajkhet, L. E. Estimation of the solutions of linear stochastic integral equations. (English. Russian original) Zbl 0684.93080 J. Appl. Math. Mech. 51, No. 5, 607-612 (1987); translation from Prikl. Mat. Mekh. 51, No. 5, 775-781 (1987). Reviewer: W.Rümelin MSC: 93E11 60G35 93C30 PDFBibTeX XMLCite \textit{V. B. Kolmanovskij} and \textit{L. E. Shajkhet}, J. Appl. Math. Mech. 51, No. 5, 607--612 (1987; Zbl 0684.93080); translation from Prikl. Mat. Mekh. 51, No. 5, 775--781 (1987) Full Text: DOI
Shajkhet, L. E. On a necessary condition for optimality of a control for stochastic systems. (English. Russian original) Zbl 0621.93076 Theory Probab. Math. Stat. 33, 117-126 (1986); translation from Teor. Veroyatn. Mat. Stat. 33, 104-113 (1985). MSC: 93E20 49K45 60H10 60H05 PDFBibTeX XMLCite \textit{L. E. Shajkhet}, Theory Probab. Math. Stat. 33, 117--126 (1986; Zbl 0621.93076); translation from Teor. Veroyatn. Mat. Stat. 33, 104--113 (1985)
Shaĭkhet, L. E. On equations determining the moments of solutions of linear stochastic equations with delay. (Russian) Zbl 0436.60046 Teor. Sluch. Protsess. 6, 120-123 (1978). MSC: 60H10 60J65 PDFBibTeX XMLCite \textit{L. E. Shaĭkhet}, Teor. Sluch. Protsess. 6, 120--123 (1978; Zbl 0436.60046)