Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations
(PDEs) associated to them have been widely used in models from engineering, finance, and …

In his forward-looking paper [374] at the conference “Mathematics Towards the Third
Millennium,” our esteemed colleague at Brown University Prof. David Mumford argued that …

The well-known stochastic Lotka–Volterra model for interacting multi-species in ecology has
some typical features: highly nonlinear, positive solution and multi-dimensional. The known …

For a function g (h), we write g (h)= O (hp) to mean that there exist constants h0> 0 and K> 0
(independent of h) such that| g (h)|< Khp for all| h|< h0. In words, this means that g (h) tends …

We develop a perturbation theory for stochastic differential equations (SDEs) by which we
mean both stochastic ordinary differential equations (SODEs) and stochastic partial …

Solving stochastic differential equations (SDEs) numerically, explicit Euler–Maruyama (EM)
schemes are used most frequently under global Lipschitz conditions for both drift and …

This paper is concerned with the numerical approximation of stochastic ordinary differential
equations, which satisfy a global monotonicity condition. This condition includes several …

This paper proposes an adaptive timestep construction for an Euler–Maruyama
approximation of SDEs with nonglobally Lipschitz drift. It is proved that if the timestep is …

In this paper, we derive fully implementable first-order time-stepping schemes for McKean–
Vlasov stochastic differential equations, allowing for a drift term with super-linear growth in …

We extend the taming techniques for explicit Euler approximations of stochastic differential
equations driven by Lévy noise with superlinearly growing drift coefficients. Strong …