Sequential Testing for Simple Hypotheses for Processes Driven by Fractional Brownian Motion

REFERENCES

• Kleptsyna , M. L. , and Le Breton , A. ( 2002 ). Statistical Analysis of the Fractional Ornstein-Uhlenbeck Type Process . Statistical Inference for Stochastic Processes 5 : 229 – 248 .
   Google Scholar
• Kleptsyna , M. L. , Le Breton , A. , and Roubaud , M.-C. ( 2000a ). General Approach to Filtering with Fractional Brownian Noises–-Application to Linear Systems . Stochastics and Stochastic Reports 71 : 119 – 140 .
   Google Scholar
• Kleptsyna , M. L. , Le Breton , A. , and Roubaud , M.-C. ( 2000b ). Parameter Estimation and Optimal Filtering for Fractional Type Stochastic Systems . Statistical Inference for Stochastic Processes 3 : 173 – 182 . [CROSSREF]
   Google Scholar
• Le Breton , A. ( 1998 ). Filtering and Parameter estimation in a Simple Linear Model Driven by a Fractional Brownian Motion . Statistics and Probability Letters 38 : 263 – 274 . [CROSSREF]
   Web of Science ®Google Scholar
• Liptser , R. S. , and Shiryayev , A. N. ( 2001a ). Statistics of Random Processes I: General Theory , second edition , Berlin : Springer-Verlag .
   Google Scholar
• Liptser , R. S. , and Shiryayev , A. N. ( 2001b ). Statistics of Random Processes II: Applications , second edition , Berlin : Springer-Verlag .
   Google Scholar
• Norros , I. , Valkeila , E. , and Virtamo , J. ( 1999 ). An Elementary Approach to a Girsanov Type Formula and Other Analytical Results on Fractional Brownian Motion . Bernoulli 5 : 571 – 587 .
   Web of Science ®Google Scholar
• Novikov , A. A. ( 1972 ). Sequential Estimation of the Parameters of Diffusion Processes . Mathematical Notes 12 : 812 – 818 .
   Google Scholar
• Prakasa Rao , B. L. S. ( 1999a ). Statistical Inference for Diffusion Type Processes , London and New York : Arnold and Oxford University Press .
   Google Scholar
• Prakasa Rao , B. L. S. ( 1999b ). Semimartingales and Their Statistical Inference , Boca Raton, Fla. and London : CRC Press and Chapman and Hall .
   Google Scholar
• Prakasa Rao , B. L. S. ( 2003a ). Parametric Estimation for Linear Stochastic Differential Equations Driven by Fractional Brownian Motion . Random Operators and Stochastic Equations 11 : 229 – 242 . [CROSSREF]
   Google Scholar
• Prakasa Rao , B. L. S. ( 2003b ). Berry-Esseen bound for MLE for Linear Stochastic Differential Equations Driven by Fractional Brownian Motion . Indian Statistical Institute , New Delhi , Preprint .
   Google Scholar
• Prakasa Rao , B. L. S. ( 2004a ). Sequential Estimation for Fractional Ornstein-Uhlenbeck Process . Sequential Analysis 23 : 33 – 44 . [CROSSREF]
   Google Scholar
• Prakasa Rao , B. L. S. ( 2004b ). Self-Similar Processes, Fractional Brownian Motion and Statistical Inference , in A Festschrift for Herman Rubin , A. Das Gupta , ed., Lecture Notes and Monograph Series 45 , pp. 98 – 125 , Beachwood Ohio : Institute of Mathematical Statistics .
   Google Scholar
• Samko , S. G. , Kilbas , A. A. , and Marichev , O. I. ( 1993 ). Fractional Integrals and Derivatives , Yverdon : Gordon and Breach Science .
   Google Scholar