اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدWeak Error for stable driven SDEs: expansion of the densities
254
0
0.0
(
0
)
تأليف
Valentin Konakov
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Consider a multidimensional SDE of the form $X_t = x+int_{0}^{t} b(X_{s-})ds+int{0}^{t} f(X_{s-})dZ_s$ where $(Z_s)_{sge 0}$ is a symmetric stable process. Under suitable assumptions on the coefficients the unique strong solution of the above equation admits a density w.r.t. the Lebesgue measure and so does its Euler scheme. Using a parametrix approach, we derive an error expansion at order 1 w.r.t. the time step for the difference of these densities.
قيم البحث
اقرأ أيضاً
We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak H{o}rmander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the associated generator
under some dimension constraints. Also, when the driving noise is scalar and tempered, we establish density bounds reflecting the multi-scale behavior of the process.
We establish the existence of smooth densities for solutions to a broad class of path-dependent SDEs under a Hormander-type condition. The classical scheme based on the reduced Malliavin matrix turns out to be unavailable in the path-dependent contex
t. We approach the problem by lifting the given $n$-dimensional path-dependent SDE into a suitable $L_p$-type Banach space in such a way that the lifted Banach-space-valued equation becomes a state-dependent reformulation of the original SDE. We then formulate Hormanders bracket condition in $mathbb R^n$ for non-anticipative SDE coefficients defining the Lie brackets in terms of vertical derivatives in the sense of the functional It^o calculus. Our pathway to the main result engages an interplay between the analysis of SDEs in Banach spaces, Malliavin calculus, and rough path techniques.
In this paper we study the asymptotic properties of the power variations of stochastic processes of the type X=Y+L, where L is an alpha-stable Levy process, and Y a perturbation which satisfies some mild Lipschitz continuity assumptions. We establish
local functional limit theorems for the power variation processes of X. In case X is a solution of a stochastic differential equation driven by L, these limit theorems provide estimators of the stability index alpha. They are applicable for instance to model fitting problems for paleo-climatic temperature time series taken from the Greenland ice core.
In this paper, the discrete parameter expansion is adopted to investigate the estimation of heat kernel for Euler-Maruyama scheme of SDEs driven by {alpha}-stable noise, which implies krylovs estimate and khasminskiis estimate. As an application, the
convergence rate of Euler-Maruyama scheme of a class of multidimensional SDEs with singular drift( in aid of Zvonkins transformation) is obtained.
The theory of one-dimensional stochastic differential equations driven by Brownian motion is classical and has been largely understood for several decades. For stochastic differential equations with jumps the picture is still incomplete, and even som
e of the most basic questions are only partially understood. In the present article we study existence and uniqueness of weak solutions to [ {rm d}Z_t=sigma(Z_{t-}){rm d} X_t ]driven by a (symmetric) $alpha$-stable Levy process, in the spirit of the classical Engelbert-Schmidt time-change approach. Extending and completing results of Zanzotto we derive a complete characterisation for existence und uniqueness of weak solutions for $alphain(0,1)$. Our approach is not based on classical stochastic calculus arguments but on the general theory of Markov processes. We proof integral tests for finiteness of path integrals under minimal assumptions.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
