An asymptotically probabilistic method for a class of partial integrodifferential equations

In this paper, we consider a nonlocal boundary condition and examine the asymptotic behavior of the solution to a family of nonlocal partial differential equations in the half-space. Our approach is fully probabilistic and builds upon the works of Huang et al. Bernoulli, 28 (2022), 1648–1674 and Diakhaby et al. Stoch. Anal. Appl., 34 (2016), 496–509. Reflected stochastic differential equations, driven by multiplicative Lévy noise and with singular coefficients, play an important role in our method.