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In this paper we study the infinite dimensional Malliavin calculus, and apply it to determing when the solution of an infinite dimensional stochastic differential equation has the property that its finite dimensional distributions possess smooth density.
This paper is a continuation of the research carried out in –, where the robustness analysis for stochastic approximation algorithms is given for two cases: 1. The regression function and the Liapunov function are not zero at the sought-forx
0; 2. lim sup
i+1 is not...
In this paper we consider global and local bifurcations in disturbed planar Hamiltonian vector fields which are invariant under a rotation over π. All calculation formulas of bifurcation curves have been obtained. Various possible distributions and the existence of limit cycles and singular...
The use of the jackknife method is successful in many situations. However, when the observations are from anm-dependent stationary process, the ordinary jackknife may provide an inconsistent variance estimator. It is shown in this note that this deficiency of the jackknife can be rectified and...
We prove that if there is a strongly connected digraph of ordern, maximum degreed, diameterk and connectivityc, thenn≤c d
k−d /d−1+d+1. It improves the previous known results, and it, in fact, is the best possible for several interesting cases. A similar result for arc connectivity is also...
LetB be a separable real Banach space andX(t) be a symmetric conservative diffusion process taking values inB. In this paper, we decompose the functionalu(X(t),t) into a sum of a square integrable martingale and a regular 0-quadratic variation process. On this basis, we establish the predictable...
Restricted to certain classes of discrete life distributions, and based on moments, conditional binomial moments, order statistics, spacing or record values, characterizations of geometric distributions are given.
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