Estimates on moments of the solutions to stochastic differential equations with respect to martingales in the plane

Let M = { M z , z ϵ R 2 +} be a two-parameter strong martingale, A be a two-parameter increasing process on R 2 + = [0, + ∞) × [0, + ∞). Consider the following stochastic differential equations in the plane: X z = X 0 + ∞ R z a(ξ,X) dM ξ + ∞ R z b(ξ,X) dA ξ for z ϵ R 2 +. Under some assumptions on t...

Full description

Saved in:
Bibliographic Details
Published inStochastic processes and their applications Vol. 62; no. 2; pp. 263 - 276
Main Authors Liang, Zong-xia, Zheng, Ming-li
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.1996
Elsevier
SeriesStochastic Processes and their Applications
Subjects
Online AccessGet full text

Cover

Loading…
More Information
Summary:Let M = { M z , z ϵ R 2 +} be a two-parameter strong martingale, A be a two-parameter increasing process on R 2 + = [0, + ∞) × [0, + ∞). Consider the following stochastic differential equations in the plane: X z = X 0 + ∞ R z a(ξ,X) dM ξ + ∞ R z b(ξ,X) dA ξ for z ϵ R 2 +. Under some assumptions on the coefficients a, b and the integrators M, A, we prove the existence and uniqueness of solutions for the equations, and obtain some estimates on moments of solution.
ISSN:0304-4149
1879-209X
DOI:10.1016/0304-4149(96)00057-9