My research focuses on stochastic numerical analysis, a field at the intersection of numerical analysis and probability theory. Stochastic elements can influence problems from various angles. First, stochasticity can arise within the model itself, accounting for uncertainties in parameters, natural variability, or external noise. This leads to stochastic differential equations, where random influences like Wiener processes drive the system.

Alternatively, randomness can be introduced through the numerical methods used to solve certain problems. Monte Carlo algorithms, for example, are effective in high-dimensional and low-regularity settings where traditional deterministic methods may struggle. Randomization also plays a crucial role in optimization, particularly in machine learning frameworks. Stochastic optimization offers key advantages, such as faster function evaluations and a reduced risk of getting stuck in local minima.

In summary, my research is centered on the numerical approximation of stochastic processes—such as solving stochastic (partial) differential equations—and on developing randomized algorithms for applications in time-stepping methods and optimization problems.