Special Issue "Unsolved Problems in Stability and Optimal Control Theory of Stochastic Systems"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 30 November 2023 | Viewed by 511

Special Issue Editor

Department of Mathematics, Ariel University, Ariel 40700, Israel
Interests: stability of stochastic functional-differential equations and stochastic Volterra difference equations; method of Lyapunov functionals construction for stability investigation; numerical analysis; optimal control

Special Issue Information

Dear Colleagues,

A host of unsolved mathematics problems have been the topic of varied research (see [1–8]), some for over 40 years, others just in 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 emerged for any of these problems to date.

The aim of this Special Issue of Symmetry on “Unsolved Problems in Stability and Optimal Control Theory of Stochastic Systems” is to collect and present contributions considering unsolved problems in mathematics. In particular, studies in the areas of, but not limited to, Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and symmetries of partial differential equations are of interest.


[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/AL1307https://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.

We wait from the potential readers both ideas for solving the presented unsolved problems and also some new unsolved problems.

Prof. Dr. Leonid Shaikhet
Guest Editor

Manuscript Submission Information

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  • stochastic hereditary systems
  • stochastic differential equation with varying delay
  • stochastic difference equation with continuous time
  • stochastic hyperbolic equation
  • two-parameter Wiener process
  • stability and optimal control

Published Papers

This special issue is now open for submission.
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