References
- Albeverio , S. , Hilbert , A. and Zehnder , E. 1992 . Hamiltonian systems with a stochastic force: Nonlinear versus linear, and a Girsanov formula . Stochastics and Stochastics Reports , 39 : 159 – 188 .
- Arnold , L. and Kliemann , W. 1986 . “ On unique ergodicity for degenerate diffusions ” . In Bremen Report , Vol. 147 , Bremen : Forschungsschwerpunkt Dynamische Systeme .
- Albeverio , S. and Klar , A. 1994 . Long time behaviour of nonlinear stochastic oscillators: the one dimensional Hamiltonian case . J. Math. Phys. , 35 : 4005 – 4027 .
- Albeverio , S. and Klar , A. 1993 . “ Stationary behaviour of stochastic Hamiltonian systems ” . In the multidimensional case Bochum Preprint
- Azéma , J. , Kaplan-Duflo , M. and Revuz , D. 1966 . Récurrence fine des processus de Markov . Ann. Inst. Henri Poincaré Sec.B , 2 ( 3 ) : 185 – 220 .
- Arnold , L. 1973 . “ Stochastic Differential Equations ” . New York : John Wiley and Sons .
- Bhattacharia , R.N. 1978 . Criteria for recurrence and existence of invariant measures for multidimensional diffusions . Ann. Prob. , 6 ( 4 ) : 541 – 553 .
- Carmona , R. 1979 . Regularity properties of Schrödinger and Dirichlet semigroups . J Funct. Anal. , 33 : 259 – 296 .
- Ehrenpreis , L. 1971 . “ Fourier Analysis in Several Complex Variables ” . New York : John Wiley and Sons .
- Freidlin , M. 1985 . “ Functional Integration and Partial Differential Equations ” . Princeton University Press .
- Getoor , R.K. Transience and recurrence of Markov processes . In Séminaire de Probabilité XIV . Vol. LNM 784 , pp. 397 – 409 . Berlin : Springer Verlag .
- Hilbert , A. 1990 . “ Bounds on transition probabilities for a stochastically perturbed Hamiltonian system ” . In Stochastics and Quantum Mechanics, World Scientific Edited by: Truman , A. and Davies , I.M. 151 – 164 . Singapore
- Ichihara , K. and Kunita , H. 1974 . A classification of the second order degenerate elliptic operators and its probabilistic characterization . Zeitschrift f. Wahrscheinlichkeitstheorie verw. Geb. , 30 : 235 – 254 .
- Ikeda , N. and Watanabe , S. 1981 . “ Stochastic Differential Equations and Diffusion Processes ” . North Holland
- Khas'minskii , R.Z. “ Stochastic Stability of Differential Equations ” . In Sijthoof, Alphen aan den Rijn
- Kliemann , W. 1987 . Recurrence and invariant measures for degenerate diffusions . Ann. Prob. , 15 : 690 – 707 .
- Kolmogorov , A. 1934 . Zufällige Bewegungen . Ann. Math. , 35 ( 1 ) : 116 – 117 . (Zur Theorie der Brownschen Bewegung)
- Kolokoltsov , V. 1995 . “ A note on the long time asymptotics of the Brownian motion with applications to the theory of quantum measurement ” . In Potential Analysis Vol. 240 , Bochum Preprint No.240, appear in
- Markus , L. and Weerasinghe , A. 1988 . Stochastic oscillators . J Diff. Equ. , 21 : 288 – 314 .
- Mc Kean , H.P. 1969 . “ Stochastic Integrals ” . New York : Academic Press .
- Narita , K. 1982 . No explosion criteria for stochastic differential equations . J. Math. Soc. Japan , 34 : 192 – 203 .
- Narita , K. 1984 . Explosion time of second order Ito processes . J. Math. Analysis Appl. , 104 : 418 – 427 .
- Potter , J. 1962 . “ Some Statistical Properties of the Motion of a Nonlinear Oscillator Driven by White Noise, PhD thesis, MIT ” .
- Reed , M. and Simon , B. 1979 . “ Methods of Modern Mathematical Physics ” . In III Scattering Theory , New York : Academic Press .