  We analyze the Wasserstein distance ($W$-distance) between two probability
distributions associated with two multidimensional jump-diffusion processes.
Specifically, we analyze a temporally decoupled squared $W_2$-distance, which
provides both upper and lower bounds associated with the discrepancies in the
drift, diffusion, and jump amplitude functions between the two jump-diffusion
processes. Then, we propose a temporally decoupled squared $W_2$-distance
method for efficiently reconstructing unknown jump-diffusion processes from
data using parameterized neural networks. We further show its performance can
be enhanced by utilizing prior information on the drift function of the
jump-diffusion process. The effectiveness of our proposed reconstruction method
is demonstrated across several examples and applications.
