The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  1. S. Albeverio, A.Klar, Longtime behaviour of stochastic Hamiltonian systems: The multidimensional case, Potential Anal. 12 (2000), 281-297. MR:2001e:37083
  2. J. Azema, M. Kaplan-Dulfo, D. Revuz, Recurrence fine des processus de Markov, Ann. Inst. Henri Poincare (Ser. B) 2 (1966), 185-220. MR:33 #8029
  3. S. Albeverio, A. Hilbert, V. N. Kolokoltsov, Transience for stochastically perturbed Newton systems, Stochastics and Stochastics Reports 60 (1997), 41-55. MR:98m:60086
  4. S. Albeverio, A. Hilbert, V.N. Kolokoltsov, Estimates Uniform in Time for the Transition Probability of Diffusions with Small Drift and for Stochastically Perturbed Newton Equations, J. Theor. Probab. 12 (1999), 293-300. MR:2001e:37083
  5. S. Albeverio, A. Hilbert, E. Zehnder, Hamiltonian systems with a stochastic force: nonlinear versus linear and a Girsanov formula, Stochastics and Stochastics Reports 39 (1992), 159-188. MR:95f:60062
  6. S. Albeverio, V. N. Kolokoltsov, The rate of escape for some Gaussian processes and the scattering theory for their small perturbations, Stochastic Processes and their Applications 67 (1997), 139-159. MR:98g:81027
  7. S.E. Ethier, T. Kurtz, Markov Processes: Characterization and Convergence,Wiley, Series in Probab. Math. Stat., New York 1986. MR:88a:60130
  8. M. Freidlin, Functional Integration and Partial Differential Equations, Princeton Univ. Press, Princeton, NJ 1985. MR:87g:60066
  9. I. Gradshteyn, I. Ryzhik, Tables of Integrals, Series, and Products. Corrected and Enlarged Edition, Academic Press, San Diego, CA 1992 (4th ed.). MR:83j:33001
  10. N. Jacob, Pseudo-differential operators and Markov processes, Akademie-Verlag, Mathematical Research 94, Berlin 1996. MR:97m:60109
  11. N. Jacob, R. L. Schilling, Levy-type processes and pseudo-differential operators, in: Barndorff-Nielsen, O. E. et al. (eds.) Levy processes: Theory and Applications, Birkhauser, Boston (2001), 139-167. MR:2002c:60077
  12. D. Khoshnevisan, Z. Shi, Chung's law for integrated Brownian motion, Trans. Am. Math. Soc. 350 (1998), 4253-4264. MR:98m:60056
  13. V. N. Kolokoltsov, Stochastic Hamilton-Jacobi-Bellman equation and stochastic Hamiltonian systems, J. Dyn. Control Syst. 2 (1996), 299-379. MR:97g:49036
  14. V. N. Kolokoltsov, Application of quasi-classical method to the investigation of the Belavkin quantum filtering equation, Mat. Zametki, 50 (1991), 153-156. (English transl.: Math. Notes 50 (1991), 1204-1206.) MR:1 155 570
  15. V. N. Kolokoltsov, A note on the long time asymptotics of the Brownian motion with applications to the theory of quantum measurement, Potential Anal. 7 (1997), 759-764. MR:99c:60179
  16. V. N. Kolokoltsov, The stochastic HJB Equation and WKB Method. In: J. Gunawardena (ed.), Idempotency, Cambridge Univ. Press, Cambridge 1998, 285-302. MR:1 608 347
  17. V. N. Kolokoltsov, Localisation and analytic properties of the simplest quantum filtering equation, Rev. Math. Phys. 10 (1998), 801-828. MR:99h:60131
  18. V. N. Kolokoltsov, Semiclassical Analysis for Diffusions and Stochastic Processes, Springer, Lecture Notes Math. 1724, Berlin 2000. MR:2001f:58073
  19. V. N. Kolokoltsov, R. L. Schilling, A. E. Tyukov, Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations, submitted.
  20. V. N. Kolokoltsov, A. E. Tyukov, The rate of escape of $alpha$-stable Ornstein-Uhlenbeck processes, Markov Process. Relat. Fields 7 (2001), 603-625. MR:1 893 144
  21. R. Z. Khasminski, Ergodic properties of recurrent diffusion processes and stabilization of the solutions to the Cauchy problem for parabolic equations, Theor. Probab. Appl. 5 (1960), 179-195.
  22. T. Kurtz, F. Marchetti, Averaging stochastically perturbed Hamiltonian systems. In: M. Cranston (ed.), Stochastic analysis, Proc. Summer Research Institute on Stochastic Analysis, Am. Math. Soc., Proc. Symp. Pure Math. 57, Providence, RI 1995, 93-114. MR:96f:60098
  23. L. Markus, A. Weerasinghe, Stochastic Oscillators, J. Differ. Equations 71 (1998), 288-314. MR:89c:34061
  24. L. Mehta, Random matrices (2nd ed.), Academic Press, Boston, MA 1991.
  25. E. Nelson, Dynamical theories of Brownian motion, Princton University Press, Mathematical Notes, Princeton, NJ 1967. MR:35 #5001
  26. K. Norita, The Smoluchowski-Kramers approximation for the stochastic Lienard equation with mean-field, Adv. Appl. Prob.23 (1991), 303-316.
  27. K. Norita, Asymptotic behavior of velocity process in the Smoluchowski-Kramers approximation for stochastic differential equations, Adv. Appl. Prob. 23 (1991), 317-326.
  28. S. Olla, S. Varadhan, Scaling limit for interacting Ornstein-Uhlenbeck processes, Commun. Math. Phys. 135 (1991), 355-378. MR:92h:60154
  29. S. Olla, S. Varadhan, H. Yau, Hydrodynamical limit for a Hamiltonian system with weak noise, Commun. Math. Phys. 155 (1993), 523-560. MR:94k:60158
  30. P. Protter, Stochastic Integration and Differential Equations, Springer, Appl. Math. 21, Berlin 1990. MR:91i:60148
  31. R.L. Schilling, Growth and Holder conditions for the sample paths of Feller processes, Probab. Theor. Relat. Fields 112 (1998), 565-611. MR:99m:60131
  32. A. Truman, H. Zhao, Stochastic Hamilton-Jacobi equation end related topics. In: A.M. Etheridge (ed.), Stochastic Partial Differential Equations, Cambridge Univ. Press, LMS Lecture Notes 276, Cambridge 1995, 287-303. MR:96k:60162
  33. A. Truman, H. Zhao, The stochastic Hamilton-Jacobi equation, stochastic heat equation and Schroedinger equations. In: A. Truman, I.M. Davis, K.D. Elworthy (eds.), Stochastic Analysis and Applications, World Scientific, Singapore 1996, 441-464. MR:98b:35230

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.