On the Comparison Theorems for the Volume of Tubes in Kahlerian Manifolds

In this note we give some comparison theorems for the volume of tubes around a complex submanifold in a Kahlerian monifold.

MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.

A Comparison Theorem for Solution of the Fully Coupled Backward Stochastic Differential Equations

The comparison theorems of solutions for BSDEs in fully coupled forward-backward stochastic differential equations (FBSDEs) are studied in this paper, here in the fully coupled FBSDEs the forward SDEs are the same structure.

COMPARISON THEOREMS FOR MULTI-DIMENSIONAL GENERAL MEAN-FIELD BDSDES

In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations(BDSDEs),that is,BDSDEs whose coefficients depend not only on the solution processes but also on their law.The first part of the paper is devoted to the comparison theorem for multi-dimensional mean-field BDSDEs with Lipschitz conditions.With the help of the comparison result for the Lipschitz case we prove the existence of a solution for multi-dimensional mean-field BDSDEs with an only continuous drift coefficient of linear growth,and we also extend the comparison theorem to such BDSDEs with a continuous coefficient.

A General Converse Comparison Theorem for Backward Stochastic Differential Equation with Non-lipschitz Coefficient

In this article, we first introduce g-expectation via the solution of backward stochastic differential equation（BSDE in short） with non-Lipschitz coefficient, and give the properties of g-expectation, then we establish a general converse comparison theorem for backward stochastic differential equation with non-Lipschitz coefficient.

ON LEVIN TYPE COMPARISON THEOREMS FOR CERTAIN SECOND ORDER DIFFERENTIAL EQUATIONS

In this paper we establish Levin type comparison theorems for certain second order differential equations. The results obtained here generalize and extend some of the earlier ones related to the Levin's comparison theorems.

A Comparison Theorem and Uniqueness Theorem of Backward Doubly Stochastic Differential Equations

In this paper, we deal with one dimensional backward doubly stochastic differential equations （BDSDEs）. We obtain a comparison theorem and a uniqueness theorem for BDSDEs with continuous coefficients.

Necessary and sufficient condition for the comparison theorem of multidimensional anticipated backward stochastic differential equations

Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type:{-dY t = f(t1, Y t1 , Z t1 , Y t+δ(t) , Z t+ζ(t) )dt Z t dB t1 , t ∈ [0, T ], Y t = ξ t1 , t ∈ [T, T + K], Z t = η t1 , t ∈ [T, T + K].In this paper, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional anticipated backward stochastic differential equations with generators independent of the anticipated term of Z.

Comparison theorems on Finsler manifolds with weighted Ricci curvature bounded below

We obtain the Laplacian comparison theorem and the Bishop- Gromov comparison theorem on a Finsler manifold with the weighted Ricci curvature Ric∞ bounded below. As applications, we prove that if the weighted Ricci curvature Ri∞ is bounded below by a positive number, then the manifold must have finite fundamental group, and must be compact if the distortion is also bounded. Moreover, we give the Calabi-Yau linear volume growth theorem on a Finsler manifold with nonnegative weighted Ricci curvature.

STURM COMPARISON THEOREMS FOR SECOND ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS

In this paper, we first establish some differential inequalities and then some Sturm comparison theorems are derived for the second order neutral nonlinear differential equations. Our results generalize some classical Sturm comparison theorems.

STURM COMPARISON THEOREM OF SOLUTION FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS

In this paper, we establish some differential identities and obtain some Sturm comparison theorems for the second order nonlinear differential equation by using them.and generalize some classicial Sturm comparison theorems.

A New Comparison Theorem of Multidimensional BSDEs

In this paper, we first study a property about the generator g of Backward Stochastic Differential Equation （BSDE） when the price of contingent claims can be represented by a multidimensional BSDE in the no-arbitrage financial market. Furthermore, motivated by the behavior of agents in finance market, we introduce a new total order q on Rn and obtain a necessary and sufficient condition for comparison theorem of multidimensional BSDEs under this order. We also give some further results for q

A General Comparison Theorem for 1-dimensional Anticipated BSDEs

Anticipated backward stochastic differential equation （ABSDE） studied the first time in 2007 is a new type of stochastic differential equations. In this paper, we establish a general comparison theorem for ABSDEs.

A Necessary Condition on Comparison Theorem for One-Dimensional Stochastic Differential Equation

We consider the comparison theorem of one-dimensional stochastic differential equation with non-Lipschitz diffusion coefficient. Considering the two one-dimensional stochastic differential equations as a two-dimensional equation,we present a necessary condition such that comparison theorem holds by viscosity solution approach.

Comparison theorems for GJMS operators

In this paper,we compare the first order fractional GJMS(see Graham et al.(1992))operator P_(1) with the conformal Laplacian P_(2) on the conformal infinity of a Poincaré-Einstein manifold.We derive some inequalities between the Yamabe constants and the first eigenvalues associated with P_(1) and P_(2),and prove some rigidity theorems by characterizing the equalities.Similarly,some comparison theorems between P_(2) and the Paneitz operator P_(4) or the 6 th order GJMS operator P_(6) are also given.

On Comparison Theorem and Solutions of BSDEs for Lévy Processes

In this paper, we consider backward stochastic differential equations driven by a Levy process. A comparison theorem and an existence and uniqueness theorem of BSDEs with non-Lipschitz coefficients are obtained.

Existence, uniqueness and strict comparison theorems for BSDEs driven by RCLL martingales

The existence,uniqueness,and strict comparison for solutions to a BSDE driven by a multi-dimensional RCLL martingale are developed.The goal is to develop a general multi-asset framework encompassing a wide spectrum of non-linear financial models with jumps,including as particular cases,the setups studied by Peng and Xu[27,28]and Dumitrescu et al.[7]who dealt with BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump.

COMPARISON THEOREM OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

This paper is devoted to deriving a comparison theorem of solutions to backward doubly stochastic differential equations driven by Brownian motion and backward It?-Kunita integral. By the application of this theorem, we give an existence result of the solutions to these equations with continuous coefficients.

COMPARISON THEOREM FOR STRONG SOLUTION OF TWO-PARAMETER POISSON TYPE STOCHASTIC DIFFERENTIAL EQUATION

Ⅰ. INTRODUCTIONIn[1], we have discussed a kind of two-parameter Poisson type

COMPARISON THEOREMS AND APPLICATIONS OF OSCILLATION OF NEUTRAL DIFFERENTIAL EQUATIONS

We first establish comparison theorems of the oscillation for a higher-order neutral delaydifferential equation. By these comparison theorems, the criterion of oscillation propertiesof neutral delay differential equation is reduced to that of nonneutral delay differential equa-tion, from which we give a series of oscillation theorems for neutral delay differentialequation.