A Conditional Independence Property for the Solution of a Linear Stochastic Differential Equation with Lateral Conditions

1998 ◽  
pp. 159-173
Author(s):  
Aureli Alabert ◽  
Marco Ferrante
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Conditional Independence ◽  
Independence Property ◽  
Linear Stochastic Differential Equation

A piecewise linear stochastic differential equation driven by a Lévy process

2011 ◽  
Vol 48 (A) ◽  
pp. 109-119 ◽  
Author(s):  
Josh Reed ◽  
Bert Zwart
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Lévy Process ◽  
Piecewise Linear ◽  
Levy Process ◽  
Invariant Distribution ◽  
Linear Drift ◽  
Linear Stochastic Differential Equation ◽  
And Storage

We consider a stochastic differential equation (SDE) with piecewise linear drift driven by a spectrally one-sided Lévy process. We show that this SDE has some connections with queueing and storage models, and we use this observation to obtain the invariant distribution.

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