Teresa Różańska

Teresa Różańska completed her doctorate at the Faculty of Mathematics and Computer Science of the University of Wrocław, where her dissertation developed a theory of stochastic integration for processes with values in UMD Banach spaces. The work established sharp decoupling inequalities for stochastic integrals driven by cylindrical Brownian motion and, more generally, by square-integrable martingales with values in Hilbert spaces, characterising the class of integrands for which the stochastic integral is well-defined as a Banach-space-valued local martingale. The central technical contribution — a set of necessary and sufficient conditions on the geometry of the target Banach space for the decoupling inequality to hold — resolved an open question connecting the Unconditionality of Martingale Differences property to the boundedness of the stochastic integral in the Itô-type framework. She subsequently held a postdoctoral fellowship at the Faculty of Mathematics of Universität Bielefeld, where she worked on maximal regularity for stochastic parabolic equations and on the connection between Banach space geometry and stochastic evolution equation theory.

Following the postdoctoral period, Różańska developed a maximal regularity theory for stochastic parabolic equations in UMD function spaces, establishing space-time Lp bounds on solutions of linear stochastic PDEs analogous to the deterministic maximal regularity results of Amann and Prüss. These bounds have direct applications to the local existence and regularity theory for nonlinear stochastic evolution equations, including the stochastic Navier-Stokes equation and reaction-diffusion systems driven by multiplicative noise. A complementary line of work extended Itô's formula to processes with values in infinite-dimensional UMD spaces, providing a general calculus framework for stochastic evolution equations that subsumes the classical Hilbert space case while applying to a substantially broader class of function spaces.

At IADU, Różańska contributes stochastic analysis foundations to the Institute's research programme in infinite-dimensional control and stochastic evolution equations. Her work supports the rigorous treatment of Hamilton-Jacobi-Bellman equations in Banach function spaces that arise when the state of an optimal control problem includes a continuous history or a spatial distribution, and underpins the technical foundations of the Institute's research on mean field systems driven by spatial stochastic dynamics.