Double Subordination Preserving Properties for a New Generalized Srivastava-Attiya Integral Operator

The authors obtain subordination and superordination preserving properties for a new defined generalized operator involving the Srivastava-Attiya integral operator.Differential sandwich-type theorems f...     

On some applications of the Briot-Bouquet differential subordination

Recently Srivastava et al. [J. Dziok, H.M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct. 14 (2003) 7-18; J. Dziok, H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999) 1-13; Y.C. Kim, H.M. Srivastava, Fractional integral and other linear operators associated with the Gaussian hypergeometric function, Complex Var. Theory Appl. 34 (1997) 293-312] introduced and studied a class of analytic functions associated with the generalized hypergeometric function. In the present paper, by using the Briot-Bouquet differential subordination, new results in this class are obtained.     

Option Pricing for Time-Change Exponential Levy Model Under Memm

The purpose of this article is to study the rational evaluation of European options price when the underlying price process is described by a time-change Levy process. European option pricing formula is obtained under the minimal entropy martingale measure （MEMM） and applied to several examples of particular time-change Levy processes. It can be seen that the framework in this paper encompasses the Black-Scholes model and almost all of the models proposed in the subordinated market.     

Sharp maximal inequalities for stochastic integrals in which the integrator is a submartingale

We obtain sharp maximal inequalities for strong subordinates of real-valued submartingales. Analogous inequalities also hold for stochastic integrals in which the integrator is a submartingale. The impossibility of general moment inequalities is also demonstrated.

     

A submartingale inequality

This paper extends Burkholder's inequality between a nonnegative submartingale and a process strongly differentially subordinate to it.

     

Capacitary Upper Estimates for Symmetric Dirichlet Forms

Upper estimates for capacities are studied for symmetric Dirichlet forms which do not necessarily admit intrinsic metric. Firstly, a general method of obtaining a sharp estimate from upper estimates for cut-off functions are provided in the local and non-local cases. Secondly, a capacitary upper estimate is established for the skew product of two symmetric Dirichlet forms for which suitable capacitary estimates are given. Several examples of capacitary upper inequalities in the local and non-local cases are also given. Especially, an upper estimate for the capacity is proved for the symmetric Dirichlet form associated to the Markov process subordinated (in the Bochner sense) to the skew product of two one-dimensional Brownian motions with respect to the local time of the first Brownian motion at the origin. This estimate is used in the recent work by the present author to establish the sharp criteria for recurrence and transience of the above-mentioned process.     

Notes on Jung-Kim-Srivastava integral operator

The object of the present paper is to investigate some properties of certain integral operator Q_β^α introduced and studied recently by Jung, Kim, and Srivastava [J. Math. Anal. Appl. 176 (1993) 138-147].     

P-叶星像函数类的一些充分条件

令Hn(p)表示形如f(z)=zp ∑ ∞k=n pakzk,且在单位圆U={z;|z|<1}内解析的函数f(z) 的全体所成的函数类.本文应用微分从属技巧得到了p-叶β级星像函数的一些充分条件,所得结果推广了一些作者的相关结果.