Necessary and sufficient conditions for existence of stationary solutions of some nonlinear stochastic systems

1990 ◽  
Vol 1 (1) ◽  
pp. 75-90
Author(s):  
W. V. Wedig ◽  
Y. K. Lin ◽  
G. Q. Cai
Keyword(s):  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Stationary Solutions ◽  
Necessary And Sufficient Conditions ◽  
Nonlinear Stochastic Systems ◽  
Necessary And Sufficient

scholarly journals Distributional properties of solutions of dVt = Vt-dUt + dLt with Lévy noise

2011 ◽  
Vol 43 (3) ◽  
pp. 688-711 ◽  
Author(s):  
Anita Diana Behme
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Autocorrelation Function ◽  
Sufficient Conditions ◽  
Stationary Solutions ◽  
Necessary And Sufficient Conditions ◽  
Tail Behavior ◽  
Absolutely Continuous ◽  
Distributional Properties ◽  
Necessary And Sufficient

For a given bivariate Lévy process (Ut, Lt)t≥0, distributional properties of the stationary solutions of the stochastic differential equation dVt = Vt-dUt + dLt are analysed. In particular, the expectation and autocorrelation function are obtained in terms of the process (U, L) and in several cases of interest the tail behavior is described. In the case where U has jumps of size −1, necessary and sufficient conditions for the law of the solutions to be (absolutely) continuous are given.

scholarly journals Distributional properties of solutions of dV t = V t-dU t + dL t with Lévy noise

2011 ◽  
Vol 43 (03) ◽  
pp. 688-711
Author(s):  
Anita Diana Behme
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Autocorrelation Function ◽  
Sufficient Conditions ◽  
Stationary Solutions ◽  
Necessary And Sufficient Conditions ◽  
Tail Behavior ◽  
Absolutely Continuous ◽  
Distributional Properties ◽  
Necessary And Sufficient

For a given bivariate Lévy process (U t , L t ) t≥0, distributional properties of the stationary solutions of the stochastic differential equation dV t = V t-dU t + dL t are analysed. In particular, the expectation and autocorrelation function are obtained in terms of the process (U, L) and in several cases of interest the tail behavior is described. In the case where U has jumps of size −1, necessary and sufficient conditions for the law of the solutions to be (absolutely) continuous are given.

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