Large Deviations Estimates for Systems with Small Noise Effects, and Applications to Stochastic Systems Theory

1986 ◽  
Vol 24 (5) ◽  
pp. 979-1008 ◽  
Author(s):  
Paul Dupuis ◽  
Harold J. Kushner
Keyword(s):  
Large Deviations ◽  
Systems Theory ◽  
Stochastic Systems ◽  
Small Noise ◽  
Noise Effects ◽  
Large Deviations Estimates

scholarly journals Viscosity methods for large deviations estimates of multiscale stochastic processes

2018 ◽  
Vol 24 (2) ◽  
pp. 605-637 ◽  
Author(s):  
Daria Ghilli
Keyword(s):  
Singular Perturbation ◽  
Large Deviations ◽  
Stochastic Processes ◽  
Stochastic Volatility ◽  
Time Scale ◽  
Stochastic Systems ◽  
Singular Perturbation Problems ◽  
Hjb Equations ◽  
Large Deviations Estimates ◽  
Perturbation Problems

We study singular perturbation problems for second order HJB equations in an unbounded setting. The main applications are large deviations estimates for the short maturity asymptotics of stochastic systems affected by a stochastic volatility, where the volatility is modelled by a process evolving at a faster time scale and satisfying some condition implying ergodicity.

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