Abstract
The martingale central limit theorem provides convergence of suitably centered and scaled sums of martingale difference sequences having finite second moments that encompass a wide range of applications that extend well beyond the classical formulations for i.i.d. summands. The approach is based upon infinitesimal conditions for a stochastic process to be a Gaussian process of interest in their own right.
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References
Billingsley P (1968) Convergence of probability measures. Wiley, New York
Brown BM (1971) Martingale central limit theorems. Ann Math Statist 42(1):59–66
Ikeda N, Watanabe S (1981) Stochastic differential equations and diffusion processes. North-Holland, Kodansha
Rosén B (1967) On the central limit theorem for sums of dependent random variables. Wahr und Verw Gebiete 7:48–52
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Bhattacharya, R., Waymire, E. (2022). Martingale Central Limit Theorem. In: Stationary Processes and Discrete Parameter Markov Processes. Graduate Texts in Mathematics, vol 293. Springer, Cham. https://doi.org/10.1007/978-3-031-00943-3_15
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DOI: https://doi.org/10.1007/978-3-031-00943-3_15
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