We propose a new, unified approach to solving jump-diffusion partial integrodifferential equations (PIDEs), which often appear in mathematical finance. Our method consists of the following steps.

The main theorems extend to matrix differential equations, Atkinson's classic theorem giving necessary and sufficient conditions for the oscillation of superlinear second-order scalar differential ...

For systems of matrix equations of the form $$U' = A(t, U, V)V,\quad V' = - B(t, U, V)$$ it is shown here that the oscillation problem can be reduced to the ...

An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...

Random matrix theory (RMT) has emerged as a powerful framework for analysing complex systems across physics, statistics and beyond, by examining the statistical properties of matrices with random ...

Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Prereq., APPM 1360 ...

Description: Finite difference methods for solving fluid flow problems. Review of classification of partial differential equations, well-posed problems, and discrete approximation of partial ...