Large deviations for stochastic fractional pantograph differential equation

The purpose of this study is to establish the Freidlin–Wentzell-type large deviation principle (LDP) for the solution of a stochastic fractional pantograph differential equation. With the Picard iterative approach, the existence of the solution is demonstrated. The indistinguishability between any two solutions of the system asserts the uniqueness. The Laplace principle, equivalent to the LDP under a Polish space, is illustrated by taking up the variational representation developed by Budhiraja and Dupuis using the weak convergence approach. The corresponding controlled deterministic system is considered to establish the compactness criterion, and validated using the sequential compactness. In accordance with Yamada–Watanabe theorem, there exists a Borel measurable function with which the weak convergence criterion is done. An example is provided to illustrate the theory developed.