Professor Ben Goldys
Ben Goldys carries out research in the area of stochastic (ordinary and partial) differential equations and their applications in Financial Mathematics and Science. A major challenge arising in sciences, finance and biology is to describe and analyze complex systems evolving randomly in space and time. Stochastic (partial) differential equations are one of the main tools to tackle with this challenge. It is a fascinating area of mathematical research involving many areas of Pure Mathematics (such as Functional Analysis, Partial Differential Equations and Ergodic Theory) in order to study complex real world problems.
Specific research areas: stochastic partial differential equations including stochastic geometric PDEs, stochastic boundary value problems, stochastic fluid dynamics, ergodic theory of infinite-dimensional diffusions, analysis on infinite-dimensional spaces, interest rate derivatives, credit risk, stochastic volatitily, mean field games, applications of stochastic control and Hamilton-Jacobi equations in Finance
Ben Goldys is a member of the Applied Mathematics Research Group
Timetable
(1) Geoemetric stochastic partial differential equations and applications in the theory of micromagnetism
(2) Mean field games and applications in Finance
(3) Stochastic boundary value problem
(4) Stochastic Navier-Stokes equation on the rotating sphere
Member of the Australian Mathematical Society
(The University of Tuebingen) Project on optimal control and numerical methods for stochastic Landau-Lifschitz-Gilbert equation | |
(LUISS University) Project on stochastic systems with memory and applications in Economics | |
(Institute of Mathematics Polish Academy of Sciences) Project on stochastic boundary value problem | |
(The University of York) Project on geometric stochastic PDEs and applications in Ferromagnetism Project on stochastic Navier-Stokes equation on the rotating sphere |
Project title | Research student |
---|---|
Using Machine Learning to Solve Stochastic Differential Equations | Nick MILTCHINOV |
Publications
Book Chapters
- Chojnowska-Michalik, A., Goldys, B. (2015). Exponential Ergodicity of Semilinear Equations Driven by Levy Processes in Hilbert Spaces. In Anna Chojnowska-Michalik, Szymon Peszat, Lukasz Stettner (Eds.), Stochastic analysis: special volume in honour of Jerzy Zabczyk, (pp. 59-72). Warsaw: Polish Academy of Sciences. [More Information]
- Zdzislaw, B., Goldys, B., Ondrejat, M. (2012). Stochastic Geometric Partial Differential Equations. In Huaizhong Zhao, Aubrey Truman (Eds.), New Trends in Stochastic Analysis and Related Topics, (pp. 1-32). Singapore: World Scientific Publishing.
- Goldys, B., Musiela, M. (2001). Infinite Dimensioanl Diffusions, Kolmogorov Equations and Interest Rate Models. In E Jouini, J Cvitanic & M Musiela (Eds.), Option Pricing, Interest Rates and Risk Management, (pp. 314-335). United Kingdom: Sage Publications.
Journals
- Brzezniak, Z., Goldys, B., Li, L. (2024). 3D stochastic Landau-Lifshitz-Gilbert equations coupled with Maxwell’s equations with full energy. Journal of Differential Equations, 390, 58-124.
- Goldys, B., Jiao, C., Le, K. (2024). Existence, uniqueness and regularity of solutions to the stochastic Landau–Lifshitz–Slonczewski equation. Journal of Evolution Equations, 24(4), 24-79. [More Information]
- Goldys, B., Peszat, S. (2024). On linear stochastic flows. Transactions of the American Mathematical Society, 377(2), 753-774. [More Information]
Conferences
- Goldys, B., Maslowski, B. (2011). On Stochastic Ergodic Control in Infinite Dimensions. 6th Seminar on Stochastic Analysis, Random Fields and Applications VI, Basel: Birkhauser. [More Information]
- Goldys, B., Maslowski, B. (2006). Exponential Ergodicity for Stochastic Reaction-Diffusion Equations. Stochastic Partial Differential Equations and Applications VII, Florida, USA: Chapman & Hall/CRC.
- Brzeznia, Z., Goldys, B., van Neerven, J. (2003). Mean square continuity of Ornstein-Uhlenbeck processes in Banach spaces. Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics, Basel: Birkhauser (imprint of Springer).
2024
- Brzezniak, Z., Goldys, B., Li, L. (2024). 3D stochastic Landau-Lifshitz-Gilbert equations coupled with Maxwell’s equations with full energy. Journal of Differential Equations, 390, 58-124.
- Goldys, B., Jiao, C., Le, K. (2024). Existence, uniqueness and regularity of solutions to the stochastic Landau–Lifshitz–Slonczewski equation. Journal of Evolution Equations, 24(4), 24-79. [More Information]
- Goldys, B., Peszat, S. (2024). On linear stochastic flows. Transactions of the American Mathematical Society, 377(2), 753-774. [More Information]
2023
- Biffs, E., Goldys, B., Prosdocimi, C., Zanella, M. (2023). A pricing formula for delayed claims: appreciating the past to value the future. Mathematics and Financial Economics, 17(2), 175-202. [More Information]
- Goldys, B., Peszat, S. (2023). Linear parabolic equation with Dirichlet white noise boundary conditions. Journal of Differential Equations, 362(Open Access), 382-437. [More Information]
2022
- Droniou, J., Goldys, B., Le, K. (2022). Design and convergence analysis of numerical methods for stochastic evolution equations with Leray–Lions operator. IMA Journal of Numerical Analysis, 42, 1143-1179. [More Information]
- Brzezniak, Z., Goldys, B., Ondrejat, M., Rana, N. (2022). Large deviations for (1 + 1)-dimensional stochastic geometric wave equation. Journal of Differential Equations, 325(Green Open Access), 1-69. [More Information]
- Goldys, B., Yang, J., Zhou, Z. (2022). Singular perturbation of zero-sum linear quadratic stochastic differential games. SIAM Journal on Control and Optimization, 60(1), 48-80. [More Information]
2020
- Brzezniak, Z., Goldys, B., Le, K. (2020). Existence of a unique solution and invariant measures for the stochastic Landau–Lifshitz–Bloch equation. Journal of Differential Equations, 269(11), 9471-9507. [More Information]
- Goldys, B., Neklyudov, M. (2020). Rescaling nonlinear noise for 1D stochastic parabolic equations. Stochastics and Dynamics, 20(4), 1-17. [More Information]
- Goldys, B., Grotowski, J., Le, K. (2020). Weak martingale solutions to the stochastic Landau-Lifshitz-Gilbert equation with multi-dimensional noise via a convergent finite-element scheme. Stochastic Processes and their Applications, 130, 232-261. [More Information]
2019
- Goldys, B., Wu, W. (2019). On a class of singular stochastic control problems driven by Levy noise. Stochastic Processes and their Applications, 129(9), 3174-3206. [More Information]
2018
- Brzezniak, Z., Goldys, B., Le Gia, Q. (2018). Random Attractors for the Stochastic Navier–Stokes Equations on the 2D Unit Sphere. Journal of Mathematical Fluid Mechanics, 20(1), 227-253. [More Information]
2017
- Brzezniak, Z., Goldys, B., Jegaraj, T. (2017). Large Deviations and Transitions Between Equilibria for Stochastic Landau–Lifshitz–Gilbert Equation. Archive for Rational Mechanics and Analysis, 226(2), 497-558. [More Information]
2016
- Goldys, B., Le, K., Tran, T. (2016). A finite element approximation for the stochastic Landau-Lifshitz-Gilbert equation. Journal of Differential Equations, 260, 937-970. [More Information]
- Goldys, B., Wu, W. (2016). Dynamic programming principle for stochastic control problems driven by general Levy noise. Stochastic Analysis and Applications, 34(6), 1083-1093. [More Information]
- Goldys, B., Peszat, S., Zabczyk, J. (2016). Gauss-Markov processes on Hilbert spaces. Transactions of the American Mathematical Society, 368(1), 89-108. [More Information]
2015
- Chojnowska-Michalik, A., Goldys, B. (2015). Exponential Ergodicity of Semilinear Equations Driven by Levy Processes in Hilbert Spaces. In Anna Chojnowska-Michalik, Szymon Peszat, Lukasz Stettner (Eds.), Stochastic analysis: special volume in honour of Jerzy Zabczyk, (pp. 59-72). Warsaw: Polish Academy of Sciences. [More Information]
- Brzeznia, Z., Goldys, B., Le Gia, Q. (2015). Random dynamical systems generated by stochastic Navier-Stokes equations on a rotating sphere. Journal of Mathematical Analysis and Applications, 426(1), 505-545. [More Information]
- Brzezniak, Z., Goldys, B., Peszat, S., Russo, F. (2015). Second order PDEs with Dirichlet white noise boundary conditions. Journal of Evolution Equations, 15(1), 1-26. [More Information]
2014
- Brze?niak, Z., Debbi, L., Goldys, B. (2014). Ergodic properties of fractional stochastic Burgers equation. Global and Stochastic Analysis, 1(2), 149-174.
- Brzezniak, Z., Goldys, B., Neklyudov, M. (2014). Multidimensional Stochastic Burgers Equation. SIAM Journal On Mathematical Analysis, 46(1), 871-889. [More Information]
2013
- Brzezniak, Z., Goldys, B., Jegaraj, T. (2013). Weak Solutions of a Stochastic Landau-Lifshitz-Gilbert Equation. Applied Mathematics Research eXpress, 2013 (1), 1-33. [More Information]
2012
- Ambrosio, L., Da Prato, G., Goldys, B., Pallara, D. (2012). Bounded Variation with Respect to a Log-Concave Measure. Communications in Partial Differential Equations, 37(12), 2272-2290. [More Information]
- Zdzislaw, B., Goldys, B., Ondrejat, M. (2012). Stochastic Geometric Partial Differential Equations. In Huaizhong Zhao, Aubrey Truman (Eds.), New Trends in Stochastic Analysis and Related Topics, (pp. 1-32). Singapore: World Scientific Publishing.
2011
- Federico, S., Goldys, B., Gozzi, F. (2011). HJB equations for the optimal control of differential equations with delays and state constraints, II: Verification and optimal feedbacks. SIAM Journal on Control and Optimization, 49(6), 2378-2414. [More Information]
- Goldys, B., Maslowski, B. (2011). On Stochastic Ergodic Control in Infinite Dimensions. 6th Seminar on Stochastic Analysis, Random Fields and Applications VI, Basel: Birkhauser. [More Information]
2010
- Federico, S., Goldys, B., Gozzi, F. (2010). HJB equations for the optimal control of differential equations with delays and state constraints, I: Regularity of viscosity solutions. SIAM Journal on Control and Optimization, 48(8), 4910-4937. [More Information]
- Brzezniak, Z., Goldys, B., Imkeller, P., Peszat, S., Priola, E., Zabczyk, J. (2010). Time irregularity of generalized Ornstein-Uhlenbeck processes. Academie des Sciences. Comptes Rendus. Mathematique, 348(5-6), 273-276. [More Information]
2009
- Fabbri, G., Goldys, B. (2009). An LQ Problem for the Heat Equation on the Halfline with Dirichlet Boundary Control and Noise. SIAM Journal on Control and Optimization, 48(3), 1473-1488. [More Information]
- Goldys, B., Neklyudov, M. (2009). Beale-Kato-Majda type condition for Burgers equation. Journal of Mathematical Analysis and Applications, 354(2), 397-411. [More Information]
- Goldys, B., Rockner, M., Zhang, X. (2009). Martingale solutions and Markov selections for stochastic partial differential equations. Stochastic Processes and their Applications, 119(5), 1725-1764. [More Information]
2008
- Goldys, B., Maslowski, B. (2008). The Ornstein-Uhlenbeck bridge and applications to Markov semigroups. Stochastic Processes and their Applications, 118(10), 1738-1767. [More Information]
2006
- Goldys, B., Maslowski, B. (2006). Exponential Ergodicity for Stochastic Reaction-Diffusion Equations. Stochastic Partial Differential Equations and Applications VII, Florida, USA: Chapman & Hall/CRC.
- Goldys, B., Maslowski, B. (2006). Lower Estimates of Transition Densities and Bounds on Exponential Ergodicity for Stochastic PDE's. Annals of Probability, 34(4), 1451-1496. [More Information]
- Bogachev, V., Goldys, B. (2006). Second Derivatives of Convex Functions in the Sense of A. D. Aleksandrov in Infinite-Dimensional Spaces with Measure. Matematicheskie Zametki, 79(4), 454-467. [More Information]
2005
- Goldys, B., Maslowski, B. (2005). Exponential ergodicity for stochastic Burgers and 2D Navier-Stokes equations. Journal of Functional Analysis, 226(1), 230-255. [More Information]
- Bogachev, V., Goldys, B. (2005). On second order derivatives of convex functions on infinite-dimensional spaces with measures. Rossiiskaya Akademiya Nauk. Doklady: svodnyi vypusk, 405(4), 439-443.
2003
- Brzeznia, Z., Goldys, B., van Neerven, J. (2003). Mean square continuity of Ornstein-Uhlenbeck processes in Banach spaces. Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics, Basel: Birkhauser (imprint of Springer).
- Goldys, B., Gozzi, F., van Neerven, J. (2003). On Closability of Directional Gradients. Potential Analysis, 18(4), 289-310. [More Information]
- Goldys, B., van Neerven, J. (2003). Transition Semigroups of Banach Space-Valued Ornstein-Uhlenbeck Processes. Acta Applicandae Mathematicae, 76(3), 283-330. [More Information]
2002
- Goldys, B., Maslowski, B. (2002). Parameter Estimation for Controlled Semilinear Stochastic Systems: Identifiability and Consistency. Journal of Multivariate Analysis, 80(2), 322-343.
- Da Prato, G., Debussche, A., Goldys, B. (2002). Some properties of invariant measures of non symmetric dissipative stochastic systems. Probability Theory and Related Fields, 123(3), 355-380. [More Information]
- Chojnowska-Michalik, A., Goldys, B. (2002). Symmetric Ornstein-Uhlenbeck semigroups and their generators. Probability Theory and Related Fields, 124(4), 459-486. [More Information]
2001
- Goldys, B., Kocan, M. (2001). Diffusion Semigroups in Spaces of Continuous Functions with Mixed Topology. Journal of Differential Equations, 173(1), 17-39. [More Information]
- Da Prato, G., Goldys, B. (2001). Elliptic operators on Rd with unbounded coefficients. Journal of Differential Equations, 172(2), 333-358.
- Duan, J., Goldys, B. (2001). Ergodicity of Stochastically Forced Large Scale Geophysical Flows. International Journal of Mathematics and Mathematical Sciences, 28(6), 313-320.
2000
- Goldys, B., Musiela, M., Sondermann, D. (2000). Lognormality of rates and term structure models. Stochastic Analysis and Applications, 18(3), 375-396. [More Information]
- Chojnowska-Michalik, A., Goldys, B. (2000). Nonsymmetric Ornstein-Uhlenbeck Generators. Infinite dimensional stochastic analysis, Amsterdam: Royal Netherlands Academy of Arts and Science.
Selected Grants
2024
- Mathematics for future magnetic devices, Goldys B, Australian Research Council (ARC)/Discovery Projects (DP)
2019
- Mathematics for breaking limits of speed and density in magnetic memories, Goldys B, Tran T, Ngan Le K, Australian Research Council (ARC)/Discovery Projects (DP)