Stochastic Volterra equations driven by cylindrical Wiener process

Journal of Evolution Equations

Volumn 7, Issue 2, 2007, Pages 373-386

  Karczewska, Anna ^a   Lizama, Carlos ^b  

^a UNIVERSITY OF ZIELONA GÓRA   (Poland)

^b UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

Author keywords

times resolvent family; Convergence of resolvent families; Stochastic convolution; Stochastic Volterra equation; Strong solution

Indexed keywords

EID: 34247567990     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-007-0302-2     Document Type: Article

References (12)

1. BAZHLEKOVA, E., Fractional Evolution Equations in Banach Spaces, Ph.D. Dissertation, Eindhoven University of Technology, 2001.
2. BONACCORSI, S. and TUJBARO, L., Mittag-Leffler's function and stochastic Volterra equations of convolution type, Stochastic Anal. Appl. 21(1) (2003), 61-78.
3. CLEMENT, PH. and DA PRATO, G., Some results on stochastic convolutions arising in Volterra equations perturbed by noise. Rend. Math. Acc. Lincei s. 9, 7 (1996), 147-153.
4. DA PRATO, G. and ZABCZYK, J., Stochastic equations in infinite dimensions, Cambridge University Press, Cambridge, 1992.
5. ENGEL, K. J. and NAGEL, R., One-parameter semigroups for linear evolution equations, Graduate texts in Mathematics 194, Springer, New York, 2000.
6. FUJTTA, Y., Integrodifferential equations which interpolates the heat equation and the wave, equation, J. Math. Phys. 30 (1989), 134-144.
7. HOLDEN, H., ØKSENDAL, B., UBØE, J. and ZHANG, T., Stochastic Partial Differential Equations: A modeling, white noise functional approach, Probability and its applicatons, Birkhäuser, 1996.
8. KARCZEWSKA, A., Properties of convolutions arising in stochastic Volterra equations, preprint: http://xxx.lanl.gov/ps/math.PR/ 0509012
9. KARCZEWSKA, A. and LIZAMA, C., Strong solutions to stochastic Volterra equations, submitted.
10. LI, M. and ZHENG, Q., On spectral inclusions and approximations of α-times resolvent families, Semigroup Forum 69 (2004), 356-368.
11. PAZY, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
12. WEIDMANN, J., Linear operators in Hilbert spaces, Springer, New York, 1980.