Stochastic Differential Equations and Applications (SDEsAPPs)

Mathematics

Stochastic Differential Equations and Applications (SDEsAPPs)

Stochastic differential equations (SDEs)

Existence, uniqueness, features, stability, analytical and numerical approximations.

Analytical approximations of solutions to SDEs; Numerical approximations of solutions to SDEs; Existence and uniqueness of solutions to SDEs and backward SDEs; Stability of solutions to SDEs; Stochastic neurotransmitter models; Convergence and divergence of numerical methods; Stochastic population and epidemiological models; Asymptotic properties of solutions to SDEs.

• STOCHASTICA, COST Association-Stochastic differential equations (SDEs) are used to model phenomena under the influence of random noise and uncertainty and are useful in an extraordinary range of applications. In health, SDE mo-dels of tumour growth can help medical practitioners design interventions. In clean energy, they can model airflow aro-und wind turbine blades, and enable multiscale modeling of entire wind farms and energy grids by representing small scale effects as noise. In computing, SDEs can be used to develop training algorithms for deep learning algorithms. The development and effective deployment of stochastic models requires input from a broad range of specialist experts: applied modelers, theoretical mathematicians, numerical analysts, and statisticians, all guided by the needs of stake-holders in academia and industry. However, in the current European research landscape, there is no large-scale frame-work enabling these communities to interact, and opportunities for goal-driven research progress that is informed by all relevant expertise are being lost. Under the umbrella of computational stochastics, STOCHASTICA will bring together members of all these communities to create a net-work of researchers with common goals informed by academic and industry partners. The work of the Action will generate a computational toolbox including a database of test problems, implementation guidance, and accessible descriptions of mathematical quality that empower non-specialist experts to make appropriate and routine use of stochastic models in applications such as natural resource management, renewable energy transmission, medical and public health applications.
• COST Action CA22108, COST Association, “Wildlife Malaria Network (WIMANET)”, 2024– Vector-borne diseases, and emerging infectious diseases of wildlife, are major contributors to the global disease burden and of increasing concern globally. Haemosporidian parasites are ubiquitous in nature, hugely diverse, and associated with morbidity and mortality across taxa, including humans, livestock and wildlife. Many research groups globally focus on these parasites as model systems for addressing a broad range of ecological and evolutionary questions with eco-nomic and health implications.
• COST Action CA23146, COST Association, “European vascular liver diseases network (EURO-VALDI-NET)”, 2024– . EURO-VALDI-NET aims to create a pan-European multidisciplinary co-operative network of stakeholders, bringing together scientists, clinicians, industry partners, and patients associations, to address the vascular liver diseases problems. Through the creation of shared data registries on main relevant basic and clinical aspects, conference calls, meetings, workshops, as well as training schools, this Action will coordinate efforts aiming at advancing the understanding of vascular liver diseases to translate basic research and preclinical findings into clinical practice.

• PCs, internet, printers, library

• 1. J. Ðorđević, K. Rognlien Dahl, Stochastic optimal control of pre-exposure prophylaxis for HIV infection for a jump model, Journal of Mathematical Biology 2024 Oct 29;89(5):55, https://link.springer.com/article/10.1007/s00285-024-02151-3.
• 2. S. Janković, J. Randjelović, M. Jovanović, Razumikhin-type exponential stability criteria of neutral stochastic functional differential equations, Journal of Mathematical Analysis and Applications 355(2) (2009) 811–820. https://doi.org/10.1016/J.JMAA.2009.02.011
• 3. M. Jovanović, M. Krstić, Stochastically perturbed vector-borne disease models with direct transmission, Applied Mathematical Modelling 36 (2012) 5214–5228. https://doi.org/10.1016/J.APM.2011.11.087
• 4. M. Krstić, M. Jovanović, On stochastic population model with the Allee effect, Mathematical and Computer Modelling, 52 (2010) 370-379. https://doi.org/10.1016/J.MCM.2010.02.051
• 5. M. Milošević, Highly nonlinear neutral stochastic differential equations with time-dependent delay and the Euler-Maruyama method, Mathematical and Computer Modelling 54 (2011) 2235-2251. https://doi.org/10.1016/j.mcm.2011.05.033

There are industry links via participation in COST actions.

• 1. A. Aman, H. Coulibaly, J. Đorđević, Forward backward stochastic differential equations with delayed generators, Stochastics and Dynamics, Vol. 23, No. 02, 2350012 (2023), DOI: https://doi.org/10.1142/S0219493723500120
• 2. C. Çetin, J. Đorđević, Approximate moment functions for logistic stochastic differential equations, Numerical Algorithms (2024). DOI: https://doi.org/10.1007/s11075-024-01911-y.
• 3. D. D. Djordjević, M. Jovanović, On the approximations of solutions to stochastic differential equations under polynomial condition, Filomat 35:1 (2021) 11-25.
• 4. D. D. Djordjević, M. Milošević, An approximate Taylor method for Stochastic Functional Differential Equations via polynomial condition, Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica 29:3 (2021) 105-133.
• 5. D. D. Djordjević, A Taylor Method for Stochastic Differential Equations with Time-Dependent Delay via the Polynomial Condition, Stochastic Analysis and Applications 40:3 (2022) 539-560.
• 6. D. D. Djordjević, B. D. Djordjević, Arbitrary-order Frechet derivatives of the exponential and logarithmic functions in real and complex Banach algebras: Applications to stochastic functional differential equations, Filomat 38:21 (2024) 7503-7524.
• 7. D. D. Djordjevic, M. Jovanović, M. Milošević, A Taylor Approximation of the Solutions of Neutral Stochastic Differential Equations With Constant Delay Under Polynomial Conditions, Journal of the Korean Mathematical Society (in the process of being published) https://doi.org/10.4134/JKMS.j240328
• 8. J. Ðorđević, Monograph: “Influences of perturbations on properties of Backward Stochastic Differential Equations” (ISBN 978-86-6275-150-8), published by Faculty of Sciences and Mathematics in Niš, 2023.
• 9. J. Ɖorđević, K. Rognlien Dahl , Stochastic optimal control of pre-exposure prophylaxis for HIV infection for a jump model, Journal of Mathematical Biology, 2024 Oct 29;89(5):55, https://link.springer.com/article/10.1007/s00285-024-02151-3.
• 10. J. Djordjevic, S. Konjik, D. Mitrovic, A. Novak, Global Controllability for Quasi- linear Non-negative Definite System of ODEs and SDEs, Journal of optimization theory and applications, (2021), Volume 190, Issue 1, 316–338, DOI: https://doi.org/10.1007/s10957-021-01886-z
• 11. J. Djordjević, S. Janković, Reflected backward stochastic differential equations with perturbations, Discrete and Continuous Dynamical System – A, Volume 38, Issue 4: (2018) 1833-1848, DOI 10.3934/dcds.2018075.
• 12. J. Ðorđević, B. Jovanović, Dynamical analysis of a stochastic delayed epidemic model with levy jumps and regime switching, Journal of the Franklin Institute 360 (2023) 1252–1283, https://doi.org/10.1016/j.jfranklin.2022.12.009.
• 13. Ј. Đorđević, B. Jovanović, Optimal Control of a Stochastic SVIR Model with Logistic Growth and Saturated Incidence Function. In: Elsadany, A.A., Adel, W., Sabbar, Y. (eds) Biology and Sustainable Development Goals. Mathematics for Sustainable Developments. Springer, Singapore (2025), https://doi.org/10.1007/978-981-96-3094-3_1.
• 14. B. Jovanović, Dynamical analysis and stationary distribution of a stochastic delayed epidemic model with Lévy jump, Mathematical Communications, 30 (2025) 1-25, https://www.mathos.unios.hr/mc.
• 15. B. Jovanović, J. Đorđević, J. Manojlović, N. Šuvak, Analysis of stability and sensitivity of deterministic and stochastic models for the spread of the new corona virus SARS-CoV-2, Filomat 35:3 (2021) 1045–1063, https://doi.org/10.2298/FIL2103045J.
• 16. M. Jovanović, S. Janković, On perturbed nonlinear Ito type stochastic integrodifferential equations, Journal of Mathematical Analysis and Applications, 269 (2002) 301-316.
• 17. M. Jovanović, S. Janković, Neutral stochastic functional differential equations with additive perturbations, Applied Mathematics and Computations, 213 (2) (2009) 370-379.
• 18. M. Jovanović, M. Krstić, Stochastically perturbed vector-borne disease models with direct transmission, Applied Mathematical Modelling 36 (2012) 5214–5228.
• 19. M. Jovanović, M. Vasilova, Dynamics of non-autonomous stochastic Gilpin–Ayala competition model with time-varying delays, Applied Mathematics and Computation 219 (2013) 6946–6964.
• 20. M. Jovanović, M. Krstić, The influence of time-dependent delay on behavior of stochastic population model with the Allee effect, Applied Mathematical Modelling 39 (2015) 733-746.
• 21. M. Jovanović, M. Krstić, Extinction in Stochastic Predator-Prey Population Model with Allee Effect on Prey, Discrete and Continuous Dynamical Systems-Series B 22(7) (2017) 2651-2667.
• 22. M. Jovanović, V. Vujović, Stability of stochastic heroin model with two distributed delays, Discrete and Continuous Dynamical Systems – B, 25(7) (2020) 2407-2432.
• 23. M. Krstić, M. Jovanović, On stochastic population model with the Allee effect, Mathematical and Computer Modelling, 52 (2010) 370-379.
• 24. M. Krstić, V. Vujović, Dynamical behaviour of the stochastic tumor-immune interaction model, Filomat, 38:25 (2024) 8773-8787.
• 25. M. Krstić, V. Vujović, M. Marković, Stationary distribution and extinction in the stochastic model of human immune system response to COVID-19 virus under regime switching, Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica 33(1) (2025) 215–237.
• 26. M. Marković, M. Krstić, On a stochastic generalized delayed SIR model with vaccination and treatment, Nonlinearity, 36(12) (2023) 7007-7024.
• 27. M. Marković, Dynamical properties of two-diffusion SIR epidemic model with Markovian switching, Open Mathematics, 23 (2025) 20240123.
• 28. M. Milošević, Almost sure exponential stability of solutions to highly nonlinear neutral stochastic differential equations with time-dependent delay and the Euler-Maruyama approximation, Mathematical and Computer Modelling 57 (2013) 887-899.
• 29. M. Milošević, An explicit analytic approximation of solutions for a class of neutral stochastic differential equations with time-dependent delay based on Taylor expansion, Applied Mathematics and Computation 274 (2016) 745-761.
• 30. M. Milošević, Divergence of the backward Euler method for ordinary stochastic differential equations, Numerical Algorithms 82(4) (2019) 1395–1407.
• 31. M. Milošević, Stochastic serotonin model with discontinuous drift, Mathematics and Computers in Simulation, 198 (2022) 359–374.
• 32. M. Milunović, M. Krstić, Long time behavior of an two diffusion stochastic SIR epidemic model with nonlinear incidence rate and treatment, Filomat, 36:8 (2022) 2829-2846.
• 33. M. Obradović, M. Milošević, Stability of a class of neutral stochastic differential equations with unbounded delay and Markovian switching and the Euler–Maruyama method, Journal of Computational and Applied Mathematics 309 (2017) 244-266.
• 34. A. Petrović, M. Milošević, The truncated Euler-Maruyama method for highly nonlinear neutral stochastic differential equations with time-dependent delay, Filomat 35:7 (2021) 2457-2484.
• 35. A. Petrović, Convergence rate of the truncated Euler-Maruyama method for highly nonlinear neutral stochastic differential equations with time-dependent delay, Open Mathematics, 22 (2024). no. 1, 20240038.
• 36. A. Petrović, M. Milošević, Strong and weak divergence of the backward Euler method for neutral stochastic differential equations with time-dependent delay, Stochastic Analysis and Applications, 42(5) (2024) 920-944.
• 37. A. Petrović, M. Milošević, Divergence of the Euler-Maruyama method for neutral stochastic differential equations with unbounded delay and Markovian switching, Numerical Algorithms (in the process of being published).
• 38. T. Trifunović, M. Jovanović, M. Milošević, The generalized Khasminskii-type conditions in establishing existence, uniqueness and moment estimates of solution to neutral stochastic functional differential equations, Filomat, 37:24 (2023) 8157–8174.

- STORM – Stochastics for Time-Space Risk Models project, Norway, 2020-2023. (J. Đorđević)
- Bilateral project with University of Osijek, Croatia, “Applied stochastic models with short term and long term structure of dependence”, 2019.-2022. (M. Jovanović, J. Đorđević, D. Djordjević, M. Milošević, M. Krstić, B. Jovanović)
- IMA – Institute for Mathematics and its Applications, University of Minneapolis, Minnesota, United States, for one month visit, June 2019. (J. Đorđević)
- Academy of Science, Kiev, Ukraine, week in November, 2021 (granted by Academy of Science Kiev & Department of Mathematics, University of Oslo). (J. Đorđević)
- Coordination and Support Activity Support for Researcher Mobility ”Modelling of the spread of diseases with time change”, granted by Research Council of Norway, for a stay of 4 months, Osijek, Croatia, January-May 2022. (J. Đorđević)
- IMSI- Institute for Mathematical and Statistical Innovation (IMSI), Chicago, United States, supported by the National Science Foundation (Grant No. DMS-1929348), April-May 2023. (J. Đorđević)
- Erasmus Plus Project “Re@WBC” – Enhancement of HE research potential contribution to further growth of the WB region, 2015–2018. (J. Đorđević)
- “Functional analysis, stochastic analysis and applications”, PMF Nis, Project No. 144003, MNTRS, 2006-2010. (M. Jovanović, M. Krstić, J. Đorđević, M. Milošević)
- “Functional analysis and applications”, PMF Nis, Project 174007, MNTRS, 2011-2020. (M. Jovanović, M. Krstić, J. Đorđević, D. Djordjević, M. Milošević, A. Petrović, B. Jovanović, M. Marković)
- DAAD scholarship, Novi Sad, Serbia, August 10 – September 10, 2016. (D. Djordjević)
-ERASMUS+ project, Staff mobility for training, University of Osijek, 10.4.2022.-15.4.2022. (M. Milošević)