Differential equations driven by fractional Brownian motion.

David Nualart; Aurel Rascanu

Collectanea Mathematica (2002)

  • Volume: 53, Issue: 1, page 55-81
  • ISSN: 0010-0757

Abstract

top
A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

How to cite

top

Nualart, David, and Rascanu, Aurel. "Differential equations driven by fractional Brownian motion.." Collectanea Mathematica 53.1 (2002): 55-81. <http://eudml.org/doc/42846>.

@article{Nualart2002,
abstract = {A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H &gt; 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.},
author = {Nualart, David, Rascanu, Aurel},
journal = {Collectanea Mathematica},
keywords = {Ecuaciones diferenciales estocásticas; Movimiento browniano; stochastic differential equations; fractional Brownian motion},
language = {eng},
number = {1},
pages = {55-81},
title = {Differential equations driven by fractional Brownian motion.},
url = {http://eudml.org/doc/42846},
volume = {53},
year = {2002},
}

TY - JOUR
AU - Nualart, David
AU - Rascanu, Aurel
TI - Differential equations driven by fractional Brownian motion.
JO - Collectanea Mathematica
PY - 2002
VL - 53
IS - 1
SP - 55
EP - 81
AB - A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H &gt; 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.
LA - eng
KW - Ecuaciones diferenciales estocásticas; Movimiento browniano; stochastic differential equations; fractional Brownian motion
UR - http://eudml.org/doc/42846
ER -

Citations in EuDML Documents

top
  1. Tianyang Nie, Aurel Răşcanu, Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion
  2. Michal Vyoral, Kolmogorov equation and large-time behaviour for fractional Brownian motion driven linear SDE's
  3. Corinne Berzin, José R. León, Estimation in models driven by fractional brownian motion
  4. A. Neuenkirch, I. Nourdin, A. Rößler, S. Tindel, Trees and asymptotic expansions for fractional stochastic differential equations
  5. A. Deya, A. Neuenkirch, S. Tindel, A Milstein-type scheme without Lévy area terms for SDEs driven by fractional brownian motion
  6. J. Šnupárková, Weak solutions to stochastic differential equations driven by fractional Brownian motion
  7. David Nualart, Stochastic calculus with respect to fractional Brownian motion
  8. Mihai Gradinaru, Ivan Nourdin, Milstein’s type schemes for fractional SDEs
  9. Fabrice Baudoin, Cheng Ouyang, Samy Tindel, Upper bounds for the density of solutions to stochastic differential equations driven by fractional brownian motions
  10. Laure Coutin, Rough paths via sewing Lemma

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.