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This research investigates the effectiveness of an Euler-based estimation method for likelihood inference in multidimensional diffusion processes.

August 13, 2026Open Access

Dimensional Asymptotics of Euler-Based Simulated Likelihood for Multidimensional Diffusions

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Randomized trial examines likelihood estimation in multidimensional diffusions, indicating crucial implications for density convergence.

This research investigates the effectiveness of an Euler-based estimation method for likelihood inference in multidimensional diffusion processes.
Evaluated the endpoint estimator's behavior using the Euler scheme and its asymptotics.
Derived exact Brownian moments and corrected density-level normalization.
Analyzed the conditions for the central limit theorem and estimator consistency across different dimensions.
Proved that the simulated density converges in probability to zero under specific conditions, contradicting previous assertions.
Demonstrated that the central limit theorem conditions fail as the estimator collapses under defined constraints.
Established consistency of the simulated maximizer in a Gaussian location model, even in conditions where density collapses.

Diogo Ribeiro (2026) studied this question.

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