Numerical Solutions of Stochastic Differential Equations with Jumps and Measurable Drifts
This paper deals with numerical analysis of solutions to stochastic differential equations
with jumps (SDEJs) with measurable drifts that may have quadratic growth. The main tool used is
the Zvonkin space transformation to eliminate the singular part of the drift. More precisely, the idea
is to transform the original SDEJs to standard SDEJs without singularity by using a deterministic
real-valued function that satisfies a second-order differential equation. The Euler–Maruyama scheme
is used to approximate the solution to the equations. It is shown that the rate of convergence is 1/2.
Numerically, two different methods are used to approximate solutions for this class of SDEJs. The
first method is the direct approximation of the original equation using the Euler–Maruyama scheme
with specific tests for the evaluation of the singular part at simulated values of the solution. The
second method consists of taking the inverse of the Euler–Maruyama approximation for Zvonkin’s
transformed SDEJ, which is free of singular terms. Comparative analysis of the two numerical
methods is carried out. Theoretical results are illustrated and proved by means of an example
This paper deals with numerical analysis of solutions to stochastic differential equations
with jumps (SDEJs) with measurable drifts that may have quadratic growth. The main tool used is…
In this paper we are interested in solving numerically quadratic SDEs with non-necessary continuous drift of the from
\begin{equation*}
X_{t}=x+\int_{0}^{t}b(s,X_{s})ds+\int_{0}^{t}f(…
We study both Malliavin regularity and numerical approximation schemes for a class of quadratic backward stochastic