A Comparison Theorem for Stochastic Equations with Integrals with Respect to Martingales and Random Measures

1983 ◽  
Vol 27 (3) ◽  
pp. 450-460 ◽  
Author(s):  
L. I. Gal’chuk
Keyword(s):  
Comparison Theorem ◽  
Stochastic Equations ◽  
Random Measures

Comparison Theorem for any Solutions of Backward Stochastic Differential Equations and its Application

2012 ◽  
Vol 524-527 ◽  
pp. 3801-3804
Author(s):  
Shi Yu Li ◽  
Wu Jun Gao ◽  
Jin Hui Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Equations ◽  
Local Martingale ◽  
One Dimensional ◽  
Lipschitz Continuous ◽  
The One ◽  
Uniformly Lipschitz

ƒIn this paper, we study the one-dimensional backward stochastic equations driven by continuous local martingale. We establish a generalized the comparison theorem for any solutions where the coefficient is uniformly Lipschitz continuous in z and is equi-continuous in y.

A COMPARISON THEOREM FOR STOCHASTIC EQUATIONS IN INFINITE DIMENSIONS AND APPLICATIONS

2010 ◽  
Vol 10 (02) ◽  
pp. 197-210
Author(s):  
NIKOLAOS HALIDIAS ◽  
MARIUSZ MICHTA
Keyword(s):  
Existence Theorem ◽  
Banach Spaces ◽  
Comparison Theorem ◽  
Stochastic Equations ◽  
Dimensional Case ◽  
Infinite Dimensions ◽  
Infinite Dimensional ◽  
Drift Coefficient

In this paper we consider stochastic equations in Banach spaces. Our first result is a comparison theorem. As an application we prove an existence theorem in the case when the drift coefficient is nonsmooth. The present studies extend some results both for deterministic and stochastic equations in infinite dimensional case.

scholarly journals A comparison theorem

1985 ◽  
Vol 106 (1) ◽  
pp. 188-195
Author(s):  
Walter Leighton
Keyword(s):  
Comparison Theorem
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