Stability of random implicit multifunctions in separable Asplund spaces

This paper is mainly devoted to present new sufficient conditions in terms of Fr acute;echet coderivatives for the local metric regularity, the metric regularity, the Lipschitzlike property, the nonemptiness and the lower semicontinuity of random implicit multifunctions in separable Asplund spaces. An example is given to illustrate the above random implicit multifunction results. Some applications to stability analysis of solution maps for random parametric generalized equations are also given.