Variations and Absolute Continuity of Set Functions on T_∞-tribe

some properties of the inclusion variation and the disjoint variation of set functions on T∞-tribe are studied in detail.The absolute continuity and singularity of set functions on T∞-tribe are discussed.The triangular norms T∞ and S∞ are considered as the operators of intersection and union between the fuzzy sets.As a result,some important conclusions about the variations and absolute continuity of set functions on T∞-tribe are obtained such as the superadditivity of inclusion variation,the relation between the variations and the equivalence proposition of absolute continuity of set functions on T∞-tribe.In addition,two small mistakes about T∞-measure are pointed out by the counterexamples and are revised.

Hypercontractivity and Absolute Continuity of Gaussian Generalized Mehler Semigroups in Hilbert Spaces

In this paper, we prove the hypercontra,ctivity of a non-differentiable Gaussian generalized Mehler semigroup using direct probabilistic argumcents, This result implics the exponential convergence of the scmigroup at infinity. Under some additional hypotheses, we also） establish the absolute continuity of the semigroup with respect to its invariant mcasure.

ABSOLUTE CONTINUITY FOR INTERACTING MEASURE-VALUED BRANCHING BROWNIAN MOTIONS

Exponential trichotomy theory is developed and the Fredholm Alternative Lemma is proved for the system with exponential trichotomies. An application of thesetheories is also given to obtain the persistence condition for heteroclinic orbits connecting nonhyperbolic equilibria, which extends the corresponding result of .

ABSOLUTE CONTINUITY OF THE OCCUPATION TIME PROCESSES WITH RESPECT TO LEBESGUE MEASURE FOR SUPER－BROWNIAN MOTION

Some properties of Super-Brownian motion have been approached by Dawson & Hochberg [1], Iscoe [2] & L3], Konno & Shiga [4] and so on. In this paper, we limit our attention to the occupation time processes of the Super-Brownian motion,and try to give an intuitive proof for their absolute continuity with respect to the Lebesgue measure on Rd (d≤3) when the initial measure of the Super-Brownian motion has the absolute continuity.

ABSOLUTE CONTINUITIES OF EXIT MEASURES AND TOTAL WEIGHTED OCCUPATION TIME MEASURES FOR SUPER-α-STABLE PROCESSES

Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xγ and Yγ are discussed.

The Loeb Algebras of Absolutely Continuous Measure

It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb algebras with respect to measure spaces (X, S,μ) and (X,S,v).

Weighted ebyev-Ostrowski type inequalities

In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new estimates on these types of inequalities.

REFINABLE DISTRIBUTIONS SUPPORTED ON SELF-AFFINE TILES

In this paper,some conditions which assure the compactly supported refinable distributions supported on a self-affine tile to be Lebesgue-Stieltjes measures or absolutely continuous measures with respect to Lebesgue-Stieltjes measures are given.

A Sufficient Condition for k′(z)(k(z)∈H^q,q≥1)to be of H^1

We proved if k(z)∈ Hª(q≥ 1),g(z) is analytic on| ≠ = 1, g(e)+ k(e") q= min g(e")+ h(e)heHq, then k' (z)∈ H' , especially, if q1, then k(z) is an analytic function on the closed unit disk| ≠1.

On the (<i>r</i>,<i>φ</i>,<i>ψ</i>)-Suzuki Contraction for the Multi-Valued Mappings

In this work we try to give a new contraction type in multi-valued mapping on complete metric spaces. We prove the existence of fixed point for (r,φ,ψ)-Suzuki contraction in such spaces. Around our paper, the function ψ is absolutely continuous, and in this case, the contraction proposed by as has a fixed point.

Nearly optimal Bayesian shrinkage for high-dimensional regression

During the past decade,shrinkage priors have received much attention in Bayesian analysis of high-dimensional data.This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,which has a heavy and flat tail and allocates a sufficiently large probability mass in a very small neighborhood of zero.While enjoying its efficiency in posterior simulations,the shrinkage prior can lead to a nearly optimal posterior contraction rate and the variable selection consistency as the spike-and-slab prior.Our numerical results show that under the posterior consistency,Bayesian methods can yield much better results in variable selection than the regularization methods such as LASSO and SCAD.This paper also establishes a BvM-type result,which leads to a convenient way of uncertainty quantification for regression coefficient estimates.

Radon Nikodym Derivative on Loeb Space

In this paper, we first show that if υ is absolutly continuous with respect to μ , i.e., υu , then L( *S, *μ)L( *S, *υ) . We also prove that υμ if and only if L( *υ)L( *μ) and d(L( *υ))/d(L( *μ))= 0( *(dμ/dυ)) . We shall define the Loeb space of σ finite measure space by a natural way and prove that the results above can be extended to σ finite measure spaces.

Stochastic Fractional Anderson Models with Fractional Noises

The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises, whose differential operators are fractional. A unique solution for the model in some appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and its HSlder continuity is studied. On the other hand, the absolute continuity of the solution is also discussed.

Smoothness of the Functional Law Generated by a Nonlinear SPDE

The authors consider a stochastic heat equation in dimension d=1 driven by an additive space time white noise and having a mild nonlinearity.It is proved that the functional law of its solution is absolutely continuous and possesses a smooth density with respect to the functional law of the corresponding linear SPDE.

Regularization by Noise for the Point Vortex Model of mSQG Equations

We consider the point vortex model associated to the modified Surface Quasi-Geostrophic(mSQG) equations on the two dimensional torus. It is known that this model is well posed for almost every initial conditions. We show that, when the system is perturbed by a certain space-dependent noise, it admits a unique global solution for any initial configuration. We also present an explicit example for the deterministic system on the plane where three different point vortices collapse.

GIRSANOV'S THEOREM ON ABSTRACT WIENER SPACES

The moments and absolute continuity of measure valued branching Brownian motions with bounded interacting intensity are investigated. An estimate of higher order moments is obtained.The absolute continuity is verified in the one dimension case. This thereby verifies the conjecture of Méléard and Roelly in .

OCCUPATION TIME PROCESSES OF FLEMING-VIOT PROCESSES

Suppose that Xt is the Fleming-Viot process associated with fractional power Laplacian operator -(-△)α/2 0 < α≥ 2, and Yt= f_0￣t Xs.ds is the so-called occupation time process.In this paper) the asymptotic behavior at a large time and the absolute continuity of Yt are investigated.

Density functions of doubly-perturbed stochastic differential equations with jumps

We consider a real-valued doubly-perturbed stochastic differential equation driven by a subordinated Brownian motion. By using classic Malliavin calculus, we prove that the law of the solution is absolutely continuous with respect to the Lebesgue measure on R.

Radon-Nikodym Theorem in Signed Loeb Space

This paper gives the Radon-Nikodym theorem in signed Loeb space under 1-saturated nonstandard model. First,the nonstandard characterization of absolute continuity is discussed,on which Radon-Nikodym theorem in signed Loeb space is obtained. Then,some facts about a finite signed Loeb measure and its variation are shown.

Decay of Correlations for Fibonacci Unimodal Interval Maps

We consider a class of generalized Fibonacci unimodal maps for which the central return times {Sn} satisfy that sn= sn-1 ＋ ksh-2 for some k≥ 1. We show that such a unimodal map admits a unique absolutely continuous invariant probability with exactly stretched exponential decay of correlations if its critical order lies in （1, k ＋ 1）.