Construction of N-particle langevin dynamics for H 1,∞- potentials via generalized dirichlet forms

Potential Analysis

Volumn 28, Issue 3, 2008, Pages 261-282

  Conrad, Florian ^a   Grothaus, Martin ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

Interacting continuous particle systems; Non sectorial diffusion processes; Periodic boundary condition

Indexed keywords

EID: 43349101106     PISSN: 09262601     EISSN: 1572929X     Source Type: Journal    
DOI: 10.1007/s11118-008-9076-6     Document Type: Article

References (22)

1. Albeverio, S., Kondratiev, Y.G., Röckner, M.: Strong Feller properties for distorted Brownian motion and applications to finite particle systems with singular interactions. In: Finite and Infinite Dimensional Analysis in Honor of Leonard Gross, vol. 317 of Contemporary Mathematics. American Mathematical Society, Providence, RI (2003)
2. Alt, H.W.: Lineare Funktionalanalysis. Springer Verlag, Berlin (2002)
3. Davies, E.B.: One-Parameter Semigroups. L.M.S. Monographs. Academic Press, London (1980)
4. de Masi, A., Ianiro, N., Pellegrinotti, A., Presutti, E.: A survey of the hydrodynamical behavior of many-particle systems. In: Nonequilibrium phenomena II: From stochastics to hydrodynamics, vol. 11 of Stud. Stat. Mech., pp. 193-294. North Holland Physics Publishing, Amsterdam (1984)
5. Dohmann, J.: Feller-type properties and path regularities of markov processes. Forum Math. 17(3), 343-359 (2005)
6. Durrett, R.: Stochastic Calculus. A Practical Introduction. CRC Press, Boca Raton (1996)
7. Fattler, T., Grothaus, M.: Strong Feller properties for distorted Brownian motion with reflecting boundary condition and an application to continuous N-particle systems with singular interactions. SFB 611 preprint 282, University of Bonn, 2006. J. Funct. Anal. 246(2):217-241 (2007)
8. Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet forms and symmetric Markov processes. W. de Gruyter, Berlin (1994)
9. Grothaus, M., Kondratiev, Y.G., Lytvynov, E., Röckner, M.: Scaling limit of stochastic dynamics in classical continuous systems. Ann. Probab. 31(3), 1494-1532 (2003)
10. Grothaus, M., Kondratiev, Y., Röckner, M.: N/V-limit for stochastic dynamics in continuous particle systems. Probab. Theory Related Fields 137, 121-160 (2007)
11. 0-Semigroups and Applications to Partial Differential Equations. Notas de matematica; 218: Serie: pre-print, Universidad de los Andes (2001)
12. Ma, Z.-M., Röckner, M.: Introduction to the Theory of (Non-Symmetric) Dirichlet Forms. Springer, Berlin (1992)
13. Olla, S., Tremoulet, C.: Equilibrium fluctuations for interacting Ornstein-Uhlenbeck particles. Comm. Math. Phys. 233(3), 463-491 (2003)
14. Reed, M., Simon, B.: Methods of Modern Mathematical Phyics I. Functional Analysis. Academic Press, New York (1980)
15. Schwabl, F.: Statistische Mechanik. Springer, Berlin (2004)
16. Spohn, H.: Equilibrium fluctuations for interacting Brownian particles. Commun. Math. Phys. 103, 1-33 (1986)
17. Stannat, W.: The theory of generalized Dirichlet forms and its applications in analysis and stochastics. Dissertation, Bielefeld, 1996. Published as Memoirs of the AMS, vol. 142, no. 678 (1999)
18. Swart, J.: Diffusions on manifolds. Lecture notes Winterschule Groß Dölln. http://www.mathematik.uni-tuebingen.de/swart/manif.ps (2000). Accessed 8 August 2005
19. Triebel, H.: Höhere Analysis. Harri Deutsch, Thun, Frankfurt am Main (1980)
20. Trutnau, G.: Stochastic calculus of generalized dirichlet forms and applications to stochastic differential equations in infinite dimensions. Osaka J. Math. 37, 315-343 (2000)
21. Trutnau, G.: On a class of non-symmetric diffusions containing fully non-symmetric distorted brownian motion. Forum Math. 15, 409-437 (2003)
22. Trutnau, G.: On hunt processes and strict capacities associated with generalized dirichlet forms. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8, 357-382 (2005)