Intermittent stochastic stabilization based on discrete-time observation with time delay

2020 ◽  
Vol 137 ◽  
pp. 104626 ◽  
Author(s):  
Lei Liu ◽  
Zhaojing Wu
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Stochastic Stabilization ◽  
Time Observation ◽  
Discrete Time Observation

Ornstein–Uhlenbeck type processes with non-normal distribution

1999 ◽  
Vol 36 (2) ◽  
pp. 389-402 ◽  
Author(s):  
Jens Ledet Jensen ◽  
Jan Pedersen
Keyword(s):  
Time Series ◽  
Normal Distribution ◽  
Explicit Expression ◽  
Discrete Time ◽  
Likelihood Function ◽  
Martingale Measure ◽  
Heavy Tailed ◽  
Time Observation ◽  
Equivalent Martingale ◽  
Discrete Time Observation

We analyse a class of diffusion models that (i) allows an explicit expression for the likelihood function of discrete time observation, (ii) allows the possibility of heavy-tailed observations, and (iii) allows an analysis of the tails of the increments. The class simply consists of transformed Ornstein–Uhlenbeck processes and is of relevance for heavy-tailed time series. We also treat the question of the existence of an equivalent martingale measure for the class of models considered.

Ornstein–Uhlenbeck type processes with non-normal distribution

1999 ◽  
Vol 36 (02) ◽  
pp. 389-402 ◽  
Author(s):  
Jens Ledet Jensen ◽  
Jan Pedersen
Keyword(s):  
Time Series ◽  
Normal Distribution ◽  
Explicit Expression ◽  
Discrete Time ◽  
Likelihood Function ◽  
Martingale Measure ◽  
Heavy Tailed ◽  
Time Observation ◽  
Equivalent Martingale ◽  
Discrete Time Observation

We analyse a class of diffusion models that (i) allows an explicit expression for the likelihood function of discrete time observation, (ii) allows the possibility of heavy-tailed observations, and (iii) allows an analysis of the tails of the increments. The class simply consists of transformed Ornstein–Uhlenbeck processes and is of relevance for heavy-tailed time series. We also treat the question of the existence of an equivalent martingale measure for the class of models considered.

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