115 research outputs found
Least squares estimator for path-dependent McKean-Vlasov SDEs via discrete-time observations
In this paper, 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 our paper 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-timeobservations to approximate the functional solution; (iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (e.g., H\"older continuous) and path-distribution dependent
Spectral gap for measure-valued diffusion processes
The spectral gap is estimated for measure-valued diffusion processes induced
by the intrinsic/extrinsic derivatives on the space of finite measures over a
Riemannian manifold. This provides explicit exponential convergence rate for
these processes to approximate the Dirichlet and Gamma distributions arising
from population genetics.Comment: 18 page
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