The Banach fixed point method for Ito stochastic differential equations

T. Barth; A. U. Kussmaul

Annales scientifiques de l'Université de Clermont. Mathématiques (1981)

  • Volume: 69, Issue: 19, page 1-8
  • ISSN: 0249-7042

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Barth, T., and Kussmaul, A. U.. "The Banach fixed point method for Ito stochastic differential equations." Annales scientifiques de l'Université de Clermont. Mathématiques 69.19 (1981): 1-8. <http://eudml.org/doc/80506>.

@article{Barth1981,
author = {Barth, T., Kussmaul, A. U.},
journal = {Annales scientifiques de l'Université de Clermont. Mathématiques},
keywords = {contraction; fixed point; existence and uniqueness of solutions},
language = {eng},
number = {19},
pages = {1-8},
publisher = {UER de Sciences exactes et naturelles de l'Université de Clermont},
title = {The Banach fixed point method for Ito stochastic differential equations},
url = {http://eudml.org/doc/80506},
volume = {69},
year = {1981},
}

TY - JOUR
AU - Barth, T.
AU - Kussmaul, A. U.
TI - The Banach fixed point method for Ito stochastic differential equations
JO - Annales scientifiques de l'Université de Clermont. Mathématiques
PY - 1981
PB - UER de Sciences exactes et naturelles de l'Université de Clermont
VL - 69
IS - 19
SP - 1
EP - 8
LA - eng
KW - contraction; fixed point; existence and uniqueness of solutions
UR - http://eudml.org/doc/80506
ER -

References

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  1. [1] Arnold, L.: Stochastic differential equations: Theory and applications. New York - London: Wiley1974 Zbl0278.60039MR443083
  2. [2] Caratheodory, C.: Vorlesungen über reelle Funktionen. Leipzig: Teubner1918 Zbl46.0376.12JFM46.0376.12
  3. [3] Doléans - Dade, C.: On the existence and unicity of solutions of stochastic integral equations. Z. Wahrscheinlichkeitstheorie Verw. Gebiete36, 93 - 101 (1976) Zbl0343.60038MR413270
  4. [4] Friedman, A.: Stochastic differential equations and applications. Vol. 1. New York - London: Academic Press1975 Zbl0323.60056MR494490
  5. [5] Kussmaul, A.U.: Stochastic integration and generalized martingales. Research Notes in Mathematics11. London- San Francisco - Melbourne: Pitman1977 Zbl0355.60045MR488281
  6. [6] Protter, P.: On the existence, uniqueness, convergence and explosions of solutions of systems of stochastic integral equations. Ann. Probability5, 2, 243 -261 (1977) Zbl0363.60044MR431380
  7. [7] Walter, W.: Gewöhnliche Differentialglelchungen. 2nd edition. Berlin - Heidelberg - New York: Springer1976 MR404729

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