[EN]The use of deterministic differential equations is among the most common ways to describe
how a system changes mathematically. However, in practice, it may be impossible
to account for all the factors that influence the system, or some of these factors may be
random in nature. In this case, it is natural to modify the deterministic model to obtain
one given by a stochastic differential equation. In recent years, there has been a growing
interest in the stochastic generalization of differential equations, stochastic differential
equations (SDEs). One reason for this is the wide-ranging applications of these equations,
which are used, e.g., in Finance to model financial derivatives, in Biology to model
the spread of diseases, in Physics to describe particle motion, and in Computer Science
for generative modeling. Another reason for the increased popularity of stochastic differential
equations is advances in computational power combined with the development of
numerical schemes, which are often required to solve these equations numerically. In this
thesis, we will focus on three aspects of SDEs: their numerical simulation, their stability,
and the approximation of associated operators.
