A Class of L,vy Driven SDEs and their Explicit Invariant Measures

被引：19
作者：
Albeverio, Sergio [1 ,2 ,3 ]
Di Persio, Luca [4 ]
Mastrogiacomo, Elisa [5 ]
Smii, Boubaker [1 ]
机构：
[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia
[2] Univ Bonn, Dept Appl Math, HCM, BiBoS,IZKS, Bonn, Germany
[3] CERFIM, Locarno, Switzerland
[4] Univ Verona, Dept Comp Sci, Str Le Grazie 15, Verona, Italy
[5] Univ Milano Bicocca, Dipartimento Stat & Metodi Quantitat, Piazza Ateneo Nuovo 1, I-20126 Milan, Italy
来源：
POTENTIAL ANALYSIS | 2016年 / 45卷 / 02期
关键词：
Stochastic differential equations; Invariant measures; Ornstein-Uhlenbeck Levy processes; Ground state transformations; Dirichlet forms; STOCHASTIC DIFFERENTIAL-EQUATIONS; GENERALIZED MEHLER SEMIGROUPS; REACTION-DIFFUSION EQUATIONS; ASYMPTOTIC EXPANSIONS; LAPLACE APPROXIMATIONS; WELL-POSEDNESS; HEAT-EQUATION; SPDES DRIVEN; SMALL NOISE; SPACE;
D O I：
10.1007/s11118-016-9544-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We describe a class of explicit invariant measures for stochastic differential equations driven by L,vy noise. We relate them to the corresponding Fokker Planck equation. In the symmetric case, we point out the relation with the theory of Dirichlet forms and generalized Schrodinger type operators.
引用
收藏
页码：229 / 259
页数：31
相关论文
共 168 条
[81]  
[Anonymous], PREPRINT
[82]  
[Anonymous], 1985, ANAL PARTIAL DIFFERE
[83]  
[Anonymous], 2009, Levy processes and stochastic calculus
[84]   Quasi Ornstein-Uhlenbeck processes [J].
Barndorff-Nielsen, Ole E. ;
Basse-O'Connor, Andreas .
BERNOULLI, 2011, 17 (03) :916-941
[85]   INVARIANT-MEASURES AND EVOLUTION-EQUATIONS FOR MARKOV-PROCESSES CHARACTERIZED VIA MARTINGALE PROBLEMS [J].
BHATT, AG ;
KARANDIKAR, RL .
ANNALS OF PROBABILITY, 1993, 21 (04) :2246-2268
[86]  
Bogachev V. I., 2011, J MATH SCI, V179, P7, DOI DOI 10.1007/s10958-011-0581-6
[87]   Stochastic FitzHugh-Nagumo equations on networks with impulsive noise [J].
Bonaccorsi, Stefano ;
Marinelli, Carlo ;
Ziglio, Giacomo .
ELECTRONIC JOURNAL OF PROBABILITY, 2008, 13 :1362-1379
[88]   Analysis of the stochastic FitzHugh-Nagumo system [J].
Bonaccorsi, Stefano ;
Mastrogiacomo, Elisa .
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2008, 11 (03) :427-446
[89]   A DELICATE LAW OF ITERATED LOGARITHM FOR NON-DECREASING STABLE PROCESSES - CORRECTION [J].
BREIMAN, L .
ANNALS OF MATHEMATICAL STATISTICS, 1970, 41 (03) :1126-&
[90]   A DELICATE LAW OF ITERATED LOGARITHM FOR NON-DECREASING STABLE PROCESSES [J].
BREIMAN, L .
ANNALS OF MATHEMATICAL STATISTICS, 1968, 39 (06) :1818-&
45678910111213