α-Wiener Bridges: Singularity of Induced Measures and Sample Path Properties

References

• Arató , M. , Pap , G. , and van Zuijlen , M.C.A. 2001 . Asymptotic inference for spatial autoregression and orthogonality of Ornstein–Uhlenbeck sheets . Computers & Mathematics with Applications 42 : 219 – 229 .
   Google Scholar
• Barczy , M. , and Pap , G. 2008 . Explicit formulas for Laplace transforms of certain functionals of some time inhomogeneous diffusions. ArXiv:0810.2930vl.
   Google Scholar
• Baxter , G. 1956 . A strong limit theorem for Gaussian processes . Proceedings of the American Mathematical Society 7 ( 3 ): 522 – 527 .
   Google Scholar
• Ben-Ari , I. , and Pinsky , R.G. 2005 . Absolute continuity/singularity and relative entropy properties for probability measures induced by diffusions on infinite time intervals . Stochastic Processes and their Applications 115 ( 2 ): 179 – 206 .
   Google Scholar
• Bauer , H. 1996 . Probability Theory . Walter de Gruyter , Berlin .
   Google Scholar
• Becker-Kern , P. 2004 . Random integral representation of operator-semi-self-similar processes with independent increments . Stochastic Processes and Their Applications 109 ( 2 ): 327 – 344 .
   Google Scholar
• Brennan , M.J. , and Schwartz , E.S. 1990 . Arbitrage in stock index futures . The Journal of Business 63 ( 1 ): S7 – S31 .
   Google Scholar
• Jacod , J. , and Shiryaev , A.N. 2003 . Limit Theorems for Stochastic Processes, . , 2nd ed Springer-Verlag , Berlin .
   Google Scholar
• Karatzas , I. , and Shreve , S.E. 1991 . Brownian Motion and Stochastic Calculus, . , 2nd ed Springer-Verlag , Berlin .
   Google Scholar
• Kurchenko , O.O. 2003 . A consistent estimate of the Hurst parameter for a fractional Brownian motion . Theory of Probability and Mathematical Statistics 67 : 97 – 106 .
   Google Scholar
• Lépingle , D. 1978 . Sur les comportement asymptotique des martingales locales . Seminaire de Probabilites XII, Lecture Notes in Mathematics 649 : 148 – 161 .
   Google Scholar
• Liptser , R.S. , and Shiryaev , A.N. 2001 . Statistics of Random Processes I. General Theory, . , 2nd ed Springer-Verlag , Berlin .
   Google Scholar
• Liptser , R.S. , and Shiryaev , A.N. 2001 . Statistics of Random Processes II. Applications, . , 2nd ed Springer-Verlag , Berlin .
   Google Scholar
• Mansuy , R. 2004 . On a one-parameter generalization of the Brownian bridge and associated quadratic functionals . Journal of Theoretical Probability 17 ( 4 ): 1021 – 1029 .
   Web of Science ®Google Scholar
• Prakasa Rao , B.L.S. 2008 . Singularity of fractional Brownian motions with different Hurst indices . Stochastic Analysis and Applications 26 ( 2 ): 334 – 337 .
   Web of Science ®Google Scholar
• Revuz , D. , and Yor , M. 2001 . Continuous Martingales and Brownian Motion, . , 3rd ed corrected 2nd printing , Springer-Verlag , Berlin .
   Google Scholar
• Shiryaev , A.N. 1989 . Probability, . , 2nd ed Springer , New York .
   Google Scholar