This paper deals with the existence and uniqueness of mild solutions to neutral stochastic delay functional integro-differential equations perturbed by a fractional Brownian motion BH, with Hurst parameter H E (1/2, ...This paper deals with the existence and uniqueness of mild solutions to neutral stochastic delay functional integro-differential equations perturbed by a fractional Brownian motion BH, with Hurst parameter H E (1/2, 1). We use the theory of resolvent operators developed by R. Grimmer to show the existence of mild solutions. An example is provided to illustrate the results of this work.展开更多
In this paper,nonparametric estimation for a stationary strongly mixing and manifoldvalued process(X_(j))is considered.In this non-Euclidean and not necessarily i.i.d setting,we propose kernel density estimators of th...In this paper,nonparametric estimation for a stationary strongly mixing and manifoldvalued process(X_(j))is considered.In this non-Euclidean and not necessarily i.i.d setting,we propose kernel density estimators of the joint probability density function,of the conditional probability density functions and of the conditional expectations of functionals of X_(j)given the past behavior of the process.We prove the strong consistency of these estimators under sufficient conditions,and we illustrate their performance through simulation studies and real data analysis.展开更多
文摘This paper deals with the existence and uniqueness of mild solutions to neutral stochastic delay functional integro-differential equations perturbed by a fractional Brownian motion BH, with Hurst parameter H E (1/2, 1). We use the theory of resolvent operators developed by R. Grimmer to show the existence of mild solutions. An example is provided to illustrate the results of this work.
文摘In this paper,nonparametric estimation for a stationary strongly mixing and manifoldvalued process(X_(j))is considered.In this non-Euclidean and not necessarily i.i.d setting,we propose kernel density estimators of the joint probability density function,of the conditional probability density functions and of the conditional expectations of functionals of X_(j)given the past behavior of the process.We prove the strong consistency of these estimators under sufficient conditions,and we illustrate their performance through simulation studies and real data analysis.