Reciprocal diffusions and stochastic differential equations of second orderFootnote^∗

^∗Research Supported in Part by NSF Under DMS-8601635 and AFOSR Under 85-0267

References

• Bernstein , S. “ Sur les laisons entre les grandeurs aleatoires ” . In Proc. of Int. Cong, of Math Zurich
   Google Scholar
• Schrödinger , E. 144 . “ Uber die Umkehrung der Naturgesetze ” . In Sitz. Ber. der Preuss , Vol. 1 , Akad. Wissen., Berlin Phys. Math . Zurich
   Google Scholar
• Schrodinger , E. 1932 . Theorie relativiste de l'electron et Interpretation de la mechan- ique quantique . Ann. Inst. H. Poincare , 2 : 269 – 310 .
   Google Scholar
• Slepian , D. 1961 . First passage time for a particular Gaussian process . Ann. Math. Statist , 32 : 610 – 612 .
   Google Scholar
• Jamison , B. 1974 . Reciprocal processes . Z. Wahrsch. Gebiete , 30 : 65 – 86 .
   Web of Science ®Google Scholar
• Jamison , B. 1975 . The Markov processes of Schrodinger . Z. Wahrsch. Gebiete , 32 : 323 – 331 .
   Google Scholar
• Jamison , D. 1970 . Reciprocal processes:The stationary Gaussian case . , Ann. Math. Stat. , 41 : 1624 – 1630 .
   Google Scholar
• Chay , S. C. 1972 . On quasi-Markov random fields . J. Multivar. Anal , 2 : 14 – 76 .
   Google Scholar
• Abrahams , J. and Thomas , J. B. 1981 . Some comments on conditionally Markov and reciprocal Gaussian processes . IEEE Trans. Information Theory , IT-27 : 523 – 525 .
   Web of Science ®Google Scholar
• Adler , R. J. 1981 . The Geometry of Random Fields , Edited by: Adler , R. J. New York : Wiley .
   Google Scholar
• Carmichael , J. P. , Masse , J.C. and Theodorescu , R. 1982 . Processus Gaussiens stationnaires reciproques sur un intervalle . C.R. Acad. Sci. Paris, Ser, I , 295 : 291 – 293 .
   Google Scholar
• Carmichael , J. P. , Masse , J.C. and Theodorescu , R. 1984 . Multivariate reciprocal stationary Gaussian processes, Preprint , Quebec : Laval Univ., Dept. Math .
   Google Scholar
• Carmichael , J. P. , Masse , J.C. and Theodorescu , R. 1986 . Representations for multivariate reciprocal Gaussian processes, Preprint , Quebec : Laval Univ., Dept. Math .
   Google Scholar
• Krener , A. J. 1986 . “ Reciprocal processes and the stochastic realization problem for acausal systems, in ” . In Modelling, Identification and Robust Control Edited by: Byrnes , C.I. and Lindquist , A. 197 – 211 . North-Holland
   Google Scholar
• Krener , A. J. 1986 . “ Realizations of reciprocal processes ” . In Proceedings 11 AS A Conf. on Modeling and Adaptive Control Sopron
   Google Scholar
• Miroshin , R. N. 1979 . Second-order Markov and reciprocal stationary Gaussian processes . Theor. Prob. Appl , 24 : 845 – 852 .
   Web of Science ®Google Scholar
• Abrahams , J. 1984 . On Miroshin's second-order reciprocal processes . SI AM J. Appl.Math , 44 : 190 – 192 .
   Web of Science ®Google Scholar
• Nelson , E. 1985 . Quantum Fluctuations , Princeton, , NJ : Princeton Univ. Press .
   Google Scholar
• Guerra , F. and Morato , L.M. 1983 . Quantization of dynamical systems and stochastic control theory . Phys. Rev. D , 27 : 1774 – 1786 .
   Web of Science ®Google Scholar
• Zambrini , J. C. 1986 . Stochastic mechanics according to E. Schrodinger . Phys. Rev , A33 : 1532 – 1548 .
   Google Scholar
• Zambrini , J. C. 1986 . Variational processes and stochastic versions of mechanics . J. Math. Phys , 27 : 2307 – 2330 .
   Web of Science ®Google Scholar
• Zambrini , J. C. 1987 . Euclidean quantum mechanics . Phys.Rev , A35 : 3631 – 3649 .
   Google Scholar