The solution u(t, x) of a parabolic stochastic partial differential equation is a random element of the space E α,β of Holder continuous functions on [ 0, T ] × [ 0, 1 ] of order α = 1/4 - ε in the ...

In practice the Galerkin method for solving elliptic partial differential equations yields equations involving certain integrals which cannot be evaluated analytically. Instead these integrals are ...

The goal of this course is to give a modern introduction to mathematical methods for solving hard mathematics problems that arise in the sciences. The main focus will be to explain the process of ...

Stochastic differential equations (SDEs) are at the heart of modern financial modelling, providing a framework that accommodates the inherent randomness observed in financial markets. These equations ...