FRACTIONAL BROWNIAN MOTION AND THE MARKOV PROPERTY

被引：32

作者：

Carmona, Philippe ^{[1
]}

Coutin, Laure ^{[1
]}

机构：

[1] Univ Paul Sabatier, Lab Stat & Probabil, 118 Route Narbonne, F-31062 Toulouse 4, France

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 1998年 / 3卷

关键词：

Gaussian processes; Markov Processes; Numerical Approximation; Ergodic Theorem;

D O I：

10.1214/ECP.v3-998

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：

Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This leads naturally to : An efficient algorithm to approximate the process. An ergodic theorem which applies to functionals of the type integral(t)(0)phi(V-h(s)) ds where V-h(s) = integral(s)(0) h(s - u) dB(u). and B is a real Brownian motion.

引用

页码：95 / 107

页数：13

共 50 条

[1] THE MARKOV PROPERTY OF LOCAL TIMES OF BROWNIAN MOTION INDEXED BY THE BROWNIAN TREE
Le Gall, Jean-Francois
[J]. ANNALS OF PROBABILITY, 2024, 52 (01): : 188 - 216
[2] Hurst exponents, Markov processes, and fractional Brownian motion
McCauley, Joseph L.
Gunaratne, Gemunu H.
Bassler, Kevin E.
[J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2007, 379 (01) : 1 - 9
[3] THE STRONG MARKOV PROPERTY FOR FERMION BROWNIAN-MOTION
APPLEBAUM, D
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1986, 65 (02) : 273 - 291
[4] ANOMALOUS DIFFUSION - THE THINNING PROPERTY OF FRACTIONAL BROWNIAN MOTION
Sikora, Grzegorz
[J]. ACTA PHYSICA POLONICA B, 2012, 43 (05): : 1157 - 1167
[5] LAN property for some fractional type Brownian motion
Cohen, Serge
Gamboa, Fabrice
Lacaux, Celine
Loubes, Jean-Michel
[J]. ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2013, 10 (01): : 91 - 106
[6] The fractional Brownian motion property of the atmospheric refraction index
Pérez, DG
Garavaglia, M
[J]. 4TH IBEROAMERICAN MEETING ON OPTICS AND 7TH LATIN AMERICAN MEETING ON OPTICS, LASERS, AND THEIR APPLICATIONS, 2001, 4419 : 503 - 505
[7] Is it Brownian or fractional Brownian motion?
Li, Meiyu
Gencay, Ramazan
Xue, Yi
[J]. ECONOMICS LETTERS, 2016, 145 : 52 - 55
[8] THE ABSENCE OF ARBITRAGE PROPERTY IN MIXED FRACTIONAL BROWNIAN MOTION SETTING
Halima, Hennoune
Abdeldjebbar, Kandouci
[J]. BULLETIN OF THE INSTITUTE OF MATHEMATICS ACADEMIA SINICA NEW SERIES, 2021, 16 (01): : 63 - 77
[9] Sampling fractional Brownian motion in presence of absorption: A Markov chain method
Hartmann, Alexander K.
Majumdar, Satya N.
Rosso, Alberto
[J]. PHYSICAL REVIEW E, 2013, 88 (02):
[10] A Markov additive risk process in dimension 2 perturbed by a fractional Brownian motion
Rabehasaina, Landy
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2012, 122 (08) : 2925 - 2960

← 1 2 3 4 5 →