Approximations to solutions of stochastic partial integrodifferential equations in Hilbert spaces
Moustapha Dieye1 Amadou Diop2,3 and Mamadou Moustapha Mbaye4,
1 Ecole Polytechnique de Thiès, Département Tronc commun, Thiès, Sénégal.
Sénégal
2
Classes Préparatoires aux Grandes Écoles de Thiès (CPGE), BP A10, Thiès, Sénégal.
3
Laboratoire d’Analyse Numérique et Informatique, Université Gaston Berger, Saint-Louis, Sénégal.
4
Département de Mathématiques, Faculté des Sciences et Technique, Université Cheikh Anta Diop, BP-5005, Dakar-Fann, Sénégal.
Received on March 6, 2025,
Accepted on April 22, 2025
Communicated by Gaston M. N'Guérékata
| Abstract. This work investigates the existence and uniqueness of mild solutions for a specific class of stochastic partial integrodifferential equations in Hilbert spaces by developing Picard-type approximate sequences. We provide approximate results based on Taniguchi conditions. Additionally, we apply these abstract findings to the Heath-Jarrow-Morton-Musiela (HJMM) equation to reinforce the theoretical framework. | |
| Keywords: | Stochastic processes, stochastic evolution equations, Pseudo S-asymptotically Bloch type periodic functions. |
| 2010 Mathematics Subject Classification: 34K07, 45D05, 60H20. | |