Abstract
We show the convergence of an online stochastic gradient descent estimator to obtain the drift parameter of a continuous-time jump-diffusion process. The stochastic gradient descent follows a stochastic path in the gradient direction of a function to find a minimum, which in our case determines the estimate of the unknown drift parameter. We decompose the deviation of the stochastic descent direction from the deterministic descent direction into four terms: the weak solution of the non-local Poisson equation, a Riemann integral, a stochastic integral, and a covariation term. This decomposition is employed to prove the convergence of the online estimator and we use simulations to illustrate the performance of the online estimator.
Citation
Theerawat Bhudisaksang. Álvaro Cartea. "Online drift estimation for jump-diffusion processes." Bernoulli 27 (4) 2494 - 2518, November 2021. https://doi.org/10.3150/20-BEJ1319
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