In financial and actuarial modeling and other areas of application, stochastic differential
equations with jumps have been employed to describe the dynamics of various state …

During the seven years that elapsed between the first and second editions of the present
book, considerable progress was achieved in the area of financial modelling and pricing of …

This book is a substantially revised and expanded edition reflecting major developments in
stochastic numerics since the 1st edition [314] was published in 2004. The new topics …

Some new stochastic Runge–Kutta (SRK) methods for the strong approximation of solutions
of stochastic differential equations (SDEs) with improved efficiency are introduced. Their …

“In order to make any progress, it is necessary to think of approximate techniques, and
above all, numerical algorithms... Once again, what became a major endeavor of mine, the …

We demonstrate a high-performance vendor-agnostic method for massively parallel solving
of ensembles of ordinary differential equations (ODEs) and stochastic differential equations …

A new class of stochastic Runge–Kutta methods for the weak approximation of the solution
of Itô stochastic differential equation systems with a multidimensional Wiener process is …

In this paper the sufficient conditions of existence and uniqueness of the solutions for
stochastic pantograph equation are given, ie, the local Lipschitz condition and the linear …

Inspired by recent advances in the theory of modified differential equations, we propose a
new methodology for constructing numerical integrators with high weak order for the time …

A general class of stochastic Runge-Kutta methods for the weak approximation of Itô and
Stratonovich stochastic differential equations with a multi-dimensional Wiener process is …