اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSimulation of non-Lipschitz stochastic differential equations driven by $alpha$-stable noise: a method based on deterministic homogenisation
165
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We devise an explicit method to integrate $alpha$-stable stochastic differential equations (SDEs) with non-Lipschitz coefficients. To mitigate against numerical instabilities caused by unbounded increments of the Levy noise, we use a deterministic map which has the desired SDE as its homogenised limit. Moreover, our method naturally overcomes difficulties in expressing the Marcus integral explicitly. We present an example of an SDE with a natural boundary showing that our method respects the boundary whereas Euler-Maruyama discretisation fails to do so. As a by-product we devise an entirely deterministic method to construct $alpha$-stable laws.
قيم البحث
اقرأ أيضاً
In this paper, we use a unified framework to study Poisson stable (including stationary, periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent, almost recurrent in the sense of Bebutov, Levitan almost periodic, pseudo-peri
odic, pseudo-recurrent and Poisson stable) solutions for semilinear stochastic differential equations driven by infinite dimensional Levy noise with large jumps. Under suitable conditions on drift, diffusion and jump coefficients, we prove that there exist solutions which inherit the Poisson stability of coefficients. Further we show that these solutions are globally asymptotically stable in square-mean sense. Finally, we illustrate our theoretical results by several examples.
In this paper, we study the averaging principle for a class of stochastic differential equations driven by $alpha$-stable processes with slow and fast time-scales, where $alphain(1,2)$. We prove that the strong and weak convergence order are $1-1/alp
ha$ and $1$ respectively. We show, by a simple example, that $1-1/alpha$ is the optimal strong convergence rate.
In this paper, we discuss the relationships between stability and almost periodicity for solutions of stochastic differential equations. Our essential idea is to get stability of solutions or systems by some inherited properties of Lyapunov functions
. Under suitable conditions besides Lyapunov functions, we obtain the existence of almost periodic solutions in distribution.
In this paper we present a scheme for the numerical solution of one-dimensional stochastic differential equations (SDEs) whose drift belongs to a fractional Sobolev space of negative regularity (a subspace of Schwartz distributions). We obtain a rate
of convergence in a suitable $L^1$-norm and we implement the scheme numerically. To the best of our knowledge this is the first paper to study (and implement) numerical solutions of SDEs whose drift lives in a space of distributions. As a byproduct we also obtain an estimate of the convergence rate for a numerical scheme applied to SDEs with drift in $L^p$-spaces with $pin(1,infty)$.
In this paper, we propose a monotone approximation scheme for a class of fully nonlinear partial integro-differential equations (PIDEs) which characterize the nonlinear $alpha$-stable L{e}vy processes under sublinear expectation space with $alpha in(
1,2)$. Two main results are obtained: (i) the error bounds for the monotone approximation scheme of nonlinear PIDEs, and (ii) the convergence rates of a generalized central limit theorem of Bayraktar-Munk for $alpha$-stable random variables under sublinear expectation. Our proofs use and extend techniques introduced by Krylov and Barles-Jakobsen.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
