Parabolic differential equations with unbounded coefficients - A generalization of the parametrix method

Acta Applicandae Mathematicae

Volumn 74, Issue 1, 2002, Pages 71-91

  Deck, Thomas ^a   Kruse, Susanne ^a  

^a UNIVERSITY OF MANNHEIM   (Germany)

Author keywords

Cauchy problem; Fundamental solution; Parametrix; Unbounded coefficients

Indexed keywords

HEAT CONDUCTION; PARAMETER ESTIMATION; RANDOM PROCESSES; SET THEORY;

PARABOLIC DIFFERENTIAL EQUATIONS;

DIFFERENTIAL EQUATIONS;

EID: 0036807981     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020560427405     Document Type: Article

References (18)

1. Alos, E., Leon, J.A. and Nualart, D.: Stochastic heat equation with random coefficients, Probab. Theory Related Fields 115 (1999), 41-94.
2. Aronson, D.G. and Besala, P.: Parabolic equations with unbounded coefficients, J. Differential Equations 3 (1967), 1-14.
3. Batchelor, G.K.: The Theory of Homogeneous Turbulence, Cambridge Univ. Press, 1982.
4. Besala, P.: Fundamental solution and Cauchy problem for a parabolic system with unbounded coefficients, J. Differential Equations 33 (1979), 26-38.
5. Carmona, R.A. and Cerou, F.: Transport by incompressible random velocity fields: Simulations and mathematical conjectures, In: R. Carmona and B. Rozovskii (eds), Stochastic Partial Differential Equations: Six Perspectives, Amer. Math. Soc., Providence, 1999, pp. 153-181.
6. Carmona, R.A. and Fouque, J.P.: Diffusion-Approximation for the Advection-Diffusion of a Passive Scalar by a Space-Time Gaussian Velocity Field, Progr. Probab. 36, Birkhäuser, Basel, 1995, pp. 37-49.
7. Davis, M.H.A.: Pathwise nonlinear filtering, In: Hazewinkel and Williams (eds), Stochastic Systems, the Mathematics of Filtering and Identification and Application, D. Reidel, Dordrecht, 1981.
8. Deck, T. and Potthoff, J.: On a class of stochastic partial differential equations related to turbulent transport, Probab. Theory Related Fields 111 (1998), 101-122.
9. Eidel'man, S.D.: On the Cauchy problem for parabolic systems with increasing coefficients, Dokl. Akad. Nauk SSSR 127 (1959), 760-763 (in Russian).
10. Eidel'man, S.D.: Parabolic Systems, Wiley, New York, 1962.
11. Friedman, A.: Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ, 1964.
12. Horntrop, D.J. and Majda, A.J.: Subtle statistical behavior in simple models for random advection-diffusion. J. Math. Sci. Univ. Tokyo 1 (1994), 23-70.
13. Il'in, A.M., Kalashnikov, A.S. and Oleinik, O.A.: Linear equations of the second order of parabolic type, Russian Math. Surveys 17(3) (1962), 1-143.
14. Kruse, S.: A generalized parametrix method, smoothness of random fields and application to parabolic stochastic partial differential equations, Dissertation, Universität Mannheim, 2001.
15. Leon, J.A. and Nualart, D.: Stochastic evolution equations with random generators, Ann. Probab. 26(1) (1998), 149-186.
16. Levi, E.E.: Sulle equazioni lineari totalmente ellittiche alle derivate parziali, Rend. Circ. Mat. Palermo 24 (1907), 275-317.
17. Da Prato, G. and Zabczyk, J.: Stochastic Equations in Infinite Dimensions, Cambridge Univ. Press, 1992.
18. Holden, H., Øksendal, B., Uboe, J. and Zhang, T.: Stochastic Partial differential Equations - A Modeling, White Noise Functional Approach, Birkhäuser, Basel, 1996.