TY - JOUR
T1 - Strong convergence rates for backward Euler-Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients
AU - Mao, X.
AU - Szpruch, L.
N1 - Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2013/2/1
Y1 - 2013/2/1
N2 - In this work, we generalize the current theory of strong convergence rates for the backward Euler-Maruyama scheme for highly non-linear stochastic differential equations, which appear in both mathematical finance and bio-mathematics. More precisely, we show that under a dissipative condition on the drift coefficient and super-linear growth condition on the diffusion coefficient the BEM scheme converges with strong order of a half. This type of convergence gives theoretical foundations for efficient variance reduction techniques for Monte Carlo simulations. We support our theoretical results with relevant examples, such as stochastic population models and stochastic volatility models.
AB - In this work, we generalize the current theory of strong convergence rates for the backward Euler-Maruyama scheme for highly non-linear stochastic differential equations, which appear in both mathematical finance and bio-mathematics. More precisely, we show that under a dissipative condition on the drift coefficient and super-linear growth condition on the diffusion coefficient the BEM scheme converges with strong order of a half. This type of convergence gives theoretical foundations for efficient variance reduction techniques for Monte Carlo simulations. We support our theoretical results with relevant examples, such as stochastic population models and stochastic volatility models.
UR - http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-84872506892&md5=32c1cffb4dad71cb8d8324a99282ebc8
U2 - 10.1080/17442508.2011.651213
DO - 10.1080/17442508.2011.651213
M3 - Article
AN - SCOPUS:84872506892
SN - 1744-2508
VL - 85
SP - 144
EP - 171
JO - Stochastics: An International Journal of Probability and Stochastic Processes
JF - Stochastics: An International Journal of Probability and Stochastic Processes
IS - 1
ER -