An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks
This work addresses the challenge of efficiently modeling complex stochastic processes with jumps for applications in fields like finance or physics, representing an incremental improvement by enhancing performance with prior information.
The paper tackles the problem of reconstructing unknown jump-diffusion processes from data by proposing a method based on a temporally decoupled squared Wasserstein distance, which provides bounds for discrepancies in drift, diffusion, and jump functions, and demonstrates its effectiveness across examples and applications.
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.