Paper Info
Title
Simulation-based Assessment of the stationary Tail Distribution of a stochastic differential equation.
Abstract
A commonly used approach to analyzing stochastic differential equations (SDEs) relies on performing Monte Carlo simulation with a discrete-time counterpart. In this paper we study the impact of such a time-discretization when assessing the stationary tail distribution. For a family of semi-implicit Euler discretization schemes with time-step h > 0, we quantify the relative error due to the discretization, as a function of h and the exceedance level x. By studying the existence of certain (polynomial and exponential) moments, using a sequence of prototypical examples, we demonstrate that this error may tend to 0 or ∞. The results show that the original shape of the tail can be heavily affected by the discretization. The cases studied indicate that one has to be very careful when estimating the stationary tail distribution using Euler discretization schemes.
Year
DOI
Venue
2018
10.1109/WSC.2018.8632197
WSC
Field
DocType
ISSN
Discretization,Applied mathematics,Differential equation,Monte Carlo method,Exponential function,Markov process,Polynomial,Computer science,Simulation,Euler's formula,Stochastic differential equation
Conference
0891-7736
ISBN
Citations 
PageRank 
978-1-5386-6570
0
0.34
References 
Authors
0
3
Name
Order
Citations
PageRank
Krzysztof Bisewski100.34
Daan Crommelin2157.84
Michel Mandjes353473.65