Existence of S2S^2-almost periodic solutions to a class of nonautonomous stochastic evolution equations

The paper studies the notion of Stepanov almost periodicity (or $S^2$-almost periodicity) for stochastic processes, which is weaker than the notion of quadratic-mean almost periodicity. Next, we make extensive use of the so-called Acquistapace and Terreni conditions to prove the existence and uniqueness of a Stepanov (quadratic-mean) almost periodic solution to a class of nonautonomous stochastic evolution equations on a separable real Hilbert space. Our abstract results will then be applied to study Stepanov (quadratic-mean) almost periodic solutions to a class of $n$-dimensional stochastic parabolic partial differential equations

On the Stochastic Beverton-Holt Equation with Survival Rates

The paper studies a Beverton-Holt difference equation, in which both the recruitment function and the survival rate vary randomly. It is then shown that there is a unique invariant density, which is asymptotically stable. Moreover, a basic theory for random mean almost periodic sequence on Z+ is given. Then, some suffcient conditions for the existence of a mean almost periodic solution to the stochastic Beverton-Holt equation are given

Analysis of Incomplete Longitudinal Binary Data-A Combined Markov’s Transition and Logistic Model for Non-ignorable Missingness

The problem of incomplete data is a common phenomenon in research that involves the longitudinal design approach. We investigate and develop a likelihood-based approach for incomplete longitudinal binary data using the disposition model when the missing value mechanism is non-ignorable. We combined Markov’s transition and a logistic regression model to build the dropout process and model the response using conditional logistic regression model. By holding the missingness parameter that is weakly identified constant, we analyzed their effects through a sensitivity analysis as the estimation of parameters in MLE for non-ignorable missing data is not generally plausible. An application of our approach to Schizophrenia clinical trial is presented

Regularite et proprietes limites des fonctions aleatoires a trajectoires dans D

SIGLEINIST T 77511 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Existence of almost periodic solutions for semilinear stochastic evolution equations driven by fractional Brownian motion

This article concerns the existence of almost periodic solutions to a class of abstract stochastic evolution equations driven by fractional Brownian motion in a separable real Hilbert space. Under some sufficient conditions, we establish the existence and uniqueness of a pth-mean almost periodic mild solution to those stochastic differential equations

Almost periodic random sequences in probability

This paper is concerned with almost periodic random sequences in probability. Some basic and fundamental properties of such sequences are established

Existence of almost periodic solutions to some functional integro-differential stochastic evolution equations

We investigate a class of abstract functional integro-differential stochastic evolution equations in a real separable Hilbert space. Under some suitable assumptions, we establish the existence and uniqueness of a quadratic mean almost periodic mild solution.