Paula Ozoliņa

Paula Ozoliņa is a Research Associate in the Stochastic Analysis and Control Division at the Institute for Advanced Dynamic Uncertainty. She holds a PhD in Mathematics from Latvijas Universitāte — the University of Latvia (Faculty of Physics, Mathematics and Optometry), where her doctoral research studied the regularity of solutions to degenerate parabolic PDEs of Kolmogorov type arising as the forward equations of diffusion processes with non-elliptic generators. Her thesis established Hölder continuity of weak solutions under minimal assumptions on the coefficient structure, and derived probabilistic representations of these solutions via generalised Feynman–Kac formulae applicable to diffusions with degenerate or unbounded diffusion matrices.

Ozoliņa's research is organised around the correspondence between stochastic processes and their associated PDEs: how properties of the generator — ellipticity, hypoellipticity, degeneracy — are reflected in the analytic properties of the transition density, the Green function, and the solutions to the associated Cauchy and Dirichlet problems. She has worked on backward stochastic differential equations and their connection to systems of semilinear parabolic PDEs, on the construction of weak solutions to SDEs with irregular drift via the Zvonkin transformation and its generalisations, and on well-posedness for McKean–Vlasov equations in the setting of weakly interacting diffusions.

At IADU, her research contributes to the analytical foundations of mean field models: the well-posedness of the Fokker–Planck equations that govern the evolution of agent distributions in mean field game systems, the regularity of solutions to coupled HJB–Fokker–Planck systems under degenerate diffusion, and the construction of weak solution frameworks for policy-relevant stochastic control problems with state-dependent volatility structures.