Drift-implicit Euler scheme for sandwiched processes driven by Hölder noises
Анотація
Abstract In this paper, we analyze the drift-implicit (or backward) Euler numerical scheme for a class of stochastic differential equations with unbounded drift driven by an arbitrary λ -Hölder continuous process, λ ∈ (0,1). We prove that, under some mild moment assumptions on the Hölder constant of the noise, the $L^{r}({\Omega };L^{\infty }([0,T]))$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> </mml:msup> <mml:mo>(</mml:mo> <mml:mi>Ω</mml:mi> <mml:mo>;</mml:mo> <mml:msup> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msup> <mml:mo>(</mml:mo> <mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>]</mml:mo> <mml:mo>)</mml:mo> <mml:mo>)</mml:mo> </mml:math> -approximation error converges to 0 as O (Δ λ ), Δ → 0. To exemplify, we consider numerical schemes for the generalized Cox–Ingersoll–Ross and Tsallis–Stariolo–Borland models. The results are illustrated by simulations.
Класифікація
Ідентифікатори
Рецензії (0)
Написати рецензіюРецензій ще немає. Будьте першим!
Схожі роботи
Rate of convergence of discretized drift parameters estimators in the Cox–Ingersoll–Ross model
Схоже за: Stochastic processes and financial applications · Insurance, Mortality, Demography, Risk Management
The Burgers equation driven by a stochastic measure
Схоже за: Stochastic processes and financial applications · Fluid Dynamics and Turbulent Flows
Strong solutions to stochastic equations with Lévy noise and a discontinuous drift coefficient
Схоже за: Stochastic processes and financial applications · Insurance, Mortality, Demography, Risk Management
Martingales and Super-Martingales Relative to a Convex Set of Equivalent Measures
Схоже за: Stochastic processes and financial applications · Insurance, Mortality, Demography, Risk Management
Functional limit theorems for stochastic integrals with applications to risk processes and to self-financing strategies in a multidimensional market. I
Схоже за: Stochastic processes and financial applications · Insurance, Mortality, Demography, Risk Management
On pricing and hedging in financial markets with long-range dependence
Схоже за: Stochastic processes and financial applications · Insurance, Mortality, Demography, Risk Management