Unsolved Problems in Stability and Optimal Control Theory of Stochastic Systems

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.

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.

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

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• 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