Superdiffusive limits for deterministic fast-slow dynamical systems

被引：13

作者：

Chevyrev, Ilya ^{[1
]}

Friz, Peter K. ^{[2
,3
]}

Korepanov, Alexey ^{[4
]}

Melbourne, Ian ^{[5
]}

机构：

[1] Univ Edinburgh, Sch Math, Edinburgh EH9 3FD, Midlothian, Scotland

[2] Tech Univ Berlin, Inst Math, Berlin, Germany

[3] Weierstr Inst Angew Anal & Stochast, Berlin, Germany

[4] Univ Exeter, Dept Math, Exeter EX4 4QF, Devon, England

[5] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2020年 / 178卷 / 3-4期

基金：

英国工程与自然科学研究理事会;

关键词：

DIFFERENTIAL-EQUATIONS DRIVEN; WEAK-CONVERGENCE; LEVY PROCESSES; SKEW-PRODUCT; ROUGH PATHS; P-VARIATION; THEOREMS;

D O I：

10.1007/s00440-020-00988-5

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider deterministic fast–slow dynamical systems on Rm× Y of the form {xk+1(n)=xk(n)+n-1a(xk(n))+n-1/αb(xk(n))v(yk),yk+1=f(yk),where α∈ (1 , 2). Under certain assumptions we prove convergence of the m-dimensional process Xn(t)=x⌊nt⌋(n) to the solution of the stochastic differential equation dX=a(X)dt+b(X)⋄dLα,where Lα is an α-stable Lévy process and ⋄ indicates that the stochastic integral is in the Marcus sense. In addition, we show that our assumptions are satisfied for intermittent maps f of Pomeau–Manneville type. © 2020, The Author(s).

引用

页码：735 / 770

页数：36