In this paper we consider the numerical approximation of nonlocal integro differential
parabolic equations via neural networks. These equations appear in many recent …

We consider the nonlinear Kolmogorov equation posed in a Hilbert space H, not necessarily
of finite dimension. This model was recently studied by Cox et al.[12] in the framework of …

This paper firstly investigates convergence of the backward Euler method for stochastic
differential equations (SDEs) driven by Brownian motion and compound Poisson process …

This paper first establishes a fundamental mean-square convergence theorem for general
one-step numerical approximations of L\'{e} vy noise driven stochastic differential equations …

In this paper we consider Runge–Kutta methods for jump–diffusion differential equations.
We present a study of their mean-square convergence properties for problems with …

In this paper, we consider Markov chains of the form X^n_(k+1)/n=ψ_k(X^n_k/n,Z_k+1/n,1/n)
where the innovation comes from the sequence Z_k,k∈N^∗ of independent centered …

The ever-growing appearance of infinitely divisible laws and related processes in various
areas, such as physics, mathematical biology, finance and economics, has fuelled an …

In this article, we consider multilevel Monte Carlo for the numerical computation of
expectations for stochastic differential equations driven by Lévy processes. The underlying …

In this dissertation, we consider the problem of simulation of stochastic differential equations
driven by pure jump Levy processes with infinite jump activity. Examples include, the class of …

We consider the subject of approximating tail probabilities in the general compound renewal
process framework, where severity data are assumed to follow a heavy-tailed law (in that …