Professor Ben Goldys

F07 - Carslaw Building
The University of Sydney

Telephone 9351 2976
Fax 9351 4534

Research interests

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

Teaching and supervision

Timetable

Current projects

(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

Associations

Member of the Australian Mathematical Society

International links

Germany

(The University of Tuebingen) Project on optimal control and numerical methods for stochastic Landau-Lifschitz-Gilbert equation

Italy

(LUISS University) Project on stochastic systems with memory and applications in Economics

Poland

(Institute of Mathematics Polish Academy of Sciences) Project on stochastic boundary value problem

United Kingdom

(The University of York) Project on geometric stochastic PDEs and applications in Ferromagnetism Project on stochastic Navier-Stokes equation on the rotating sphere

Selected grants

2012

  • The mathematics of novel magnetic memory materials; Goldys B; Australian Research Council (ARC)/Discovery Projects (DP).

Selected publications

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Book Chapters

  • Zdzislaw, B., Goldys, B., Ondrejat, M. (2012). Stochastic geometric partial differential equations. In Huaizhong Zhao and Aubrey Truman (Eds.), New Trends In Stochastic Analysis And Related Topics, (pp. 147-32). 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

  • 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, 2272-2290. [More Information]
  • Brzezniak, Z., Goldys, B., Jegaraj, T. (2012). Weak Solutions of a Stochastic Landau–Lifshitz–Gilbert Equation. Applied Mathematics Research eXpress, 9, 1-33. [More Information]
  • 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.
  • 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]
  • 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]
  • 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]
  • 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]
  • Goldys, B., Gozzi, F. (2006). Second order parabolic Hamilton-Jacobi-Bellman equations in Hilbert spaces and stochastic control: Lu2 approach. Stochastic Processes and their Applications, 116(12), 1932-1963. [More Information]
  • 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.
  • 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]
  • Goldys, B., Maslowski, B. (2002). Parameter Estimation for Controlled Semilinear Stochastic Systems: Identifiability and Consistency. Journal of Multivariate Analysis, 80(2), 322-343. [More Information]
  • 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]
  • 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.
  • Chojnowska-Michalik, A., Goldys, B. (2001). Generalized Ornstein-Uhlenbeck Semigroups: Littlewood-Paley-Stein and the P. A. Meyer Equivalence of Norms. Journal of Functional Analysis, 182(2), 243-279. [More Information]
  • Goldys, B. (2001). Hypercontractivity of Solutions to Hamilton-Jacobi Equations. Czechoslovak Mathematical Journal, 51(126), 733-743.
  • Goldys, B., Maslowski, B. (2001). Uniform Exponential Ergodicity of Stochastic Dissipative Systems. Czechoslovak Mathematical Journal, 51(126), 745-762.
  • Goldys, B., Musiela, M., Sondermann, D. (2000). Lognormality of rates and term structure models. Stochastic Analysis and Applications, 18(3), 375-396.

Conferences

  • Maslowski, B., Goldys, B. (2011). On Stochastic Ergodic Control in Infinite Dimensions. 6th Seminar on Stochastic Analysis, Random Fields and Applications VI, Basel: Birkhauser (imprint of Springer).
  • Goldys, B., Zhang, X. (2009). Stochastic flow for nonlinear SPDEs driven by linear multiplicative spacetime white noises. Workshop on Stochastic Analysis and Finance, Basel: Birkhauser (imprint of Springer). [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).
  • Chojnowska-Michalik, A., Goldys, B. (2000). Nonsymmetric Ornstein-Uhlenbeck Generators. Infinite dimensional stochastic analysis, Amsterdam: Royal Netherlands Academy of Arts and Science.

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, 2272-2290. [More Information]
  • Zdzislaw, B., Goldys, B., Ondrejat, M. (2012). Stochastic geometric partial differential equations. In Huaizhong Zhao and Aubrey Truman (Eds.), New Trends In Stochastic Analysis And Related Topics, (pp. 147-32). Singapore: World Scientific Publishing.
  • Brzezniak, Z., Goldys, B., Jegaraj, T. (2012). Weak Solutions of a Stochastic Landau–Lifshitz–Gilbert Equation. Applied Mathematics Research eXpress, 9, 1-33. [More Information]

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.
  • Maslowski, B., Goldys, B. (2011). On Stochastic Ergodic Control in Infinite Dimensions. 6th Seminar on Stochastic Analysis, Random Fields and Applications VI, Basel: Birkhauser (imprint of Springer).

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]
  • Goldys, B., Zhang, X. (2009). Stochastic flow for nonlinear SPDEs driven by linear multiplicative spacetime white noises. Workshop on Stochastic Analysis and Finance, Basel: Birkhauser (imprint of Springer). [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]
  • Goldys, B., Gozzi, F. (2006). Second order parabolic Hamilton-Jacobi-Bellman equations in Hilbert spaces and stochastic control: Lu2 approach. Stochastic Processes and their Applications, 116(12), 1932-1963. [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. [More Information]
  • 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.
  • Chojnowska-Michalik, A., Goldys, B. (2001). Generalized Ornstein-Uhlenbeck Semigroups: Littlewood-Paley-Stein and the P. A. Meyer Equivalence of Norms. Journal of Functional Analysis, 182(2), 243-279. [More Information]
  • Goldys, B. (2001). Hypercontractivity of Solutions to Hamilton-Jacobi Equations. Czechoslovak Mathematical Journal, 51(126), 733-743.
  • 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.
  • Goldys, B., Maslowski, B. (2001). Uniform Exponential Ergodicity of Stochastic Dissipative Systems. Czechoslovak Mathematical Journal, 51(126), 745-762.

2000

  • Goldys, B., Musiela, M., Sondermann, D. (2000). Lognormality of rates and term structure models. Stochastic Analysis and Applications, 18(3), 375-396.
  • Chojnowska-Michalik, A., Goldys, B. (2000). Nonsymmetric Ornstein-Uhlenbeck Generators. Infinite dimensional stochastic analysis, Amsterdam: Royal Netherlands Academy of Arts and Science.

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