In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for t...

this paper studies a fractional boundary value problem of nonlineardifferential equations of arbitrary orders. new existence and uniquenessresults are established using banach contraction principle. other existenceresults are obtained using schaefer and krasnoselskii fixed point theorems.in order to clarify our results, some illustrative examples are alsopresented.

The purpose of this note is to prove a central limit theorem for the L -modulus of continuity of the Brownian local time obtained in [2], using techniques of stochastic analysis. The main ingredients of the proof are an asymptotic version of Knight’s theorem and the Clark-Ocone formula for the L-modulus of the Brownian local time.

Abstract We establish a quenched local central limit theorem for the dynamic random conductance model on $${\mathbb {Z}}^d$$ Z d only assuming ergodicity with respect to space-time shifts and moment condition. As key analytic ingredient we show Hö...