LEAST SQUARES ESTIMATOR FOR PATH-DEPENDENT MCKEAN-VLASOV SDES VIA DISCRETE-TIME OBSERVATIONS

doi:10.1007/s10473-019-0305-4

摘要/Abstract

摘要： In this article, we are interested in least squares estimator for a class of path-dependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of this article lie in three aspects:(i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works; (ii) We take the advantage of linear interpolation with respect to the discrete-time observations to approximate the functional solution; (iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (for example, Hölder continuous) and path-distribution dependent.

关键词: McKean-Vlasov stochastic differential equation, tamed Euler-Maruyama scheme, weak monotonicity, least squares estimator, consistency, asymptotic distribution

Abstract: In this article, we are interested in least squares estimator for a class of path-dependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of this article lie in three aspects:(i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works; (ii) We take the advantage of linear interpolation with respect to the discrete-time observations to approximate the functional solution; (iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (for example, Hölder continuous) and path-distribution dependent.

Key words: McKean-Vlasov stochastic differential equation, tamed Euler-Maruyama scheme, weak monotonicity, least squares estimator, consistency, asymptotic distribution

中图分类号:

62F12

任盼盼, 吴奖伦. LEAST SQUARES ESTIMATOR FOR PATH-DEPENDENT MCKEAN-VLASOV SDES VIA DISCRETE-TIME OBSERVATIONS[J]. 数学物理学报(英文版), 2019, 39(3): 691-716.

Panpan REN, Jiang-Lun WU. LEAST SQUARES ESTIMATOR FOR PATH-DEPENDENT MCKEAN-VLASOV SDES VIA DISCRETE-TIME OBSERVATIONS[J]. Acta mathematica scientia,Series B, 2019, 39(3): 691-716.

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