Stationary measures for the flow of a linear differential equation driven by white noise
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- by Harry Dym PDF
- Trans. Amer. Math. Soc. 123 (1966), 130-164 Request permission
References
- Edwin F. Beckenbach and Richard Bellman, Inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 30, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. MR 0158038
- Garrett Birkhoff and Gian-Carlo Rota, Ordinary differential equations, Introductions to Higher Mathematics, Ginn and Company, Boston, Mass.-New York-Toronto, 1962. MR 0138810
- Salomon Bochner and William Ted Martin, Several Complex Variables, Princeton Mathematical Series, vol. 10, Princeton University Press, Princeton, N. J., 1948. MR 0027863
- S. Chandresekhar, Stochastic problems in physics and astronomy, Rev. Modern Phys. 15 (1943), 1–89. MR 0008130, DOI 10.1103/RevModPhys.15.1
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1955. MR 0069338
- J. L. Doob, Stochastic processes, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1990. Reprint of the 1953 original; A Wiley-Interscience Publication. MR 1038526
- J. L. Doob, The Brownian movement and stochastic equations, Ann. of Math. (2) 43 (1942), 351–369. MR 6634, DOI 10.2307/1968873
- J. L. Doob, The elementary Gaussian processes, Ann. Math. Statistics 15 (1944), 229–282. MR 10931, DOI 10.1214/aoms/1177731234
- E. B. Dynkin, Infinitesimal operators of Markov processes, Teor. Veroyatnost. i Primenen. 1 (1956), 38–60 (Russian, with English summary). MR 0089540
- F. R. Gantmacher, Matrizenrechnung. II. Spezielle Fragen und Anwendungen, Hochschulbücher für Mathematik, Band 37, VEB Deutscher Verlag der Wissenschaften, Berlin, 1959 (German). MR 0107647
- K. Ito, Lectures on stochastic processes, 2nd ed., Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 24, Distributed for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1984. Notes by K. Muralidhara Rao. MR 759892
- Kiyoshi Itô, The expected number of zeros of continuous stationary Gaussian processes, J. Math. Kyoto Univ. 3 (1963/64), 207–216. MR 166824, DOI 10.1215/kjm/1250524817
- M. Kac, Probability theory: Its role and its impact, SIAM Rev. 4 (1962), 1–11. MR 151991, DOI 10.1137/1004001
- R. Z. Has′minskiĭ, Ergodic properties of recurrent diffusion processes and stabilization of the solution of the Cauchy problem for parabolic equations, Teor. Verojatnost. i Primenen. 5 (1960), 196–214 (Russian, with English summary). MR 0133871
- Michel Loève, Probability theory, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-New York-London, 1960. 2nd ed. MR 0123342
- H. P. McKean Jr., A winding problem for a resonator driven by a white noise, J. Math. Kyoto Univ. 2 (1963), 227–235. MR 156389, DOI 10.1215/kjm/1250524936
- Gisirô Maruyama and Hiroshi Tanaka, Ergodic property of $N$-dimensional recurrent Markov processes, Mem. Fac. Sci. Kyushu Univ. Ser. A 13 (1959), 157–172. MR 112175, DOI 10.2206/kyushumfs.13.157
- Ming Chen Wang and G. E. Uhlenbeck, On the theory of the Brownian motion. II, Rev. Modern Phys. 17 (1945), 323–342. MR 0013266, DOI 10.1103/RevModPhys.17.323
- Edward Nelson, The adjoint Markoff process, Duke Math. J. 25 (1958), 671–690. MR 101555 J. Potter, Some statistical properties of the motion of a non-linear oscillator driven by white noise, Ph.D. thesis, M.I.T., Cambridge, Mass.; Trans. Amer. Math. Soc. to appear).
- Selected papers on noise and stochastic processes, Dover Publications, Inc., New York, 1954. MR 0062373
Additional Information
- © Copyright 1966 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 123 (1966), 130-164
- MSC: Primary 60.75
- DOI: https://doi.org/10.1090/S0002-9947-1966-0198541-2
- MathSciNet review: 0198541