Manuscript Topics

Problems of Stability and Optimal control are very important direction in the mathematical theory of stochastic processes. Many unsolved mathematical problems have been the subject of various studies (see [1–10]), some for more than 40 years, others only within the last few months.
Despite the broad range of publications in various journals over the years, and the various presentations in international conferences, no solutions have been found for any of these problems until now.
The aim of this Special Issue is to attract attention of researches to these problems, solutions of which will entail the essential development of a general theory of stability for stochastic functional-differential and difference equations.
We wait from the potential readers both ideas for solving the presented unsolved problems and also some new solved or unsolved problems in the theory of stability and optimal control of stochastic systems.

References  
[1] Shaikhet L. About some unsolved problems of stability theory for stochastic hereditary systems. Leverhulme International Network: Numerical and analytical solution of stochastic delay differential equations. University of Chester, UK. 31-st August to 3-rd September 2010. Abstracts, p. 6-7.  
[2] Shaikhet L. Unsolved stability problem for stochastic differential equation with varying delay. Leverhulme International Network: Numerical and analytical solution of stochastic delay differential equations. University of Chester, UK. 5-th to 7-th September 2011. Abstracts, p.21.  
[3] Shaikhet, L. About an unsolved stability problem for a stochastic difference equation with continuous time. Journal of Difference Equations and Applications. 2011, 17(3), p.441-444. (iFirst article, 2010, 14, 1563-5120, First published on 05 March 2010). doi: 10.1080/10236190903489973.  
[4] Shaikhet L. Two unsolved problems in the stability theory of stochastic differential equations with delay. Applied Mathematics Letters. 2012, V.25, N.3, p.636-637. doi:10.1016/j.aml.2011.10.002.  
[5] Shaikhet L. Some Unsolved Problems: Problem 1, Problem 2. In the book: Lyapunov functionals and stability of stochastic functional differential equations. Springer Science & Business Media, 2013, p.51-52.  
[6] Shaikhet L. About an unsolved optimal control problem for stochastic partial differential equation. XVI International Conference "Dynamical System Modeling and Stability Investigations" (DSMSI-2013), Kiev, 29-31 May 2013, p.344.  
[7] Shaikhet L. Four unsolved problems in stability and optimal control theory of stochastic systems. Academia Letters, 2021, Article https://doi.org/10.20935/AL1307; https://www.academia.edu/letters/submission.  
[8] Shaikhet L. Some unsolved problems in stability and optimal control theory of stochastic systems. Special Issue Models of Delay Differential EquationsII, MDPI Mathematics, 2022, 10(3), 474, p.1-10, https://doi.org/10.3390/math10030474. Pub.online: 01 Feb 2022.  
[9] Shaikhet L. About an unsolved problem of stabilization by noise for difference equations. MDPI, Mathematics, 2024, 12(1), 110, 11 p. https://www.mdpi.com/2227-7390/12/1/110.  
[10] Shaikhet L. Unsolved problem about stability of stochastic difference equations with continuous time and distributed delay. Modern Stochastics: Theory and Applications, 2024, 11(4), https://www.vmsta.org/journal/VMSTA/article/299/info.

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