The study of Stochastic Partial Differential Equations (SPDEs) occupies a central position in the modern analysis of physical systems where randomness and uncertainty play crucial roles. By ...

This is a preview. Log in through your library . Abstract It is frequently the case that a white-noise-driven parabolic and/or hyperbolic stochastic partial differential equation (SPDE) can have ...

Parabolic and hyperbolic stochastic partial differential equations in one-dimensional space have been proposed as models for the term structure of interest rates. The solution to these equations is ...

Stochastic processes are at the center of probability theory, both from a theoretical and an applied viewpoint. Stochastic processes have applications in many disciplines such as physics, computer ...

In this topic, our goal is to utilise and further develop the theory of non-linear PDEs to understand singular phenomena arising in geometry and in the description of the physical world. Particular ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

A partial differential equation (PDE) is a mathematical equation that involves multiple independent variables, an unknown function that is dependent on those variables, and partial derivatives of the ...

Jeremy Quastel, a professor in the department of mathematics in the Faculty of Arts & Science, has been awarded the inaugural Paul Lévy Prize in Probability by the European Mathematical Society. The ...