A variation of constant formula for Caputo fractional stochastic differential equations

By P. T. Anh, Thai Son Doan, Phan Thi Huong. Statistics and Probability Letters, 2019

53 citations recorded by the source corpus.

Abstract We establish and prove a variation of constant formula for Caputo fractional stochastic differential equations whose coefficients satisfy a standard Lipschitz condition. The main ingredient in the proof is to use Ito’s representation theorem and the known variation of constant formula for deterministic Caputo fractional differential equations. As a consequence, for these systems we point out the coincidence between the notion of classical solutions introduced in Wang et al. (2016) and mild solutions introduced in Sakthivel et al. (2013).

Subfields: Applied Mathematics, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/14c74a42a5e6bc95b6b138f2da475140e019a004