scholarly journals The Global Solutions and Moment Boundedness of Stochastic Multipantograph Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Maosheng Tian ◽  
Xuejing Meng ◽  
Jihong Chen ◽  
Xiaoqi Tang
Keyword(s):  
Lyapunov Function ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Polynomial Growth ◽  
Global Solutions ◽  
Growth Conditions ◽  
Unbounded Delay ◽  
Moment Boundedness ◽  
Methods And Techniques

We consider the existence of global solutions and their moment boundedness for stochastic multipantograph equations. By the idea of Lyapunov function, we impose some polynomial growth conditions on the coefficients of the equation which enables us to study the boundedness more applicably. Methods and techniques developed here have the potential to be applied in other unbounded delay stochastic differential equations.

scholarly journals Stabilization of Stochastic Differential Equations Driven by G-Brownian Motion with Aperiodically Intermittent Control

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 988
Author(s):  
Pengju Duan
Keyword(s):  
Brownian Motion ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Mild Solution ◽  
Intermittent Control

The paper is devoted to studying the exponential stability of a mild solution of stochastic differential equations driven by G-Brownian motion with an aperiodically intermittent control. The aperiodically intermittent control is added into the drift coefficients, when intermittent intervals and coefficients satisfy suitable conditions; by use of the G-Lyapunov function, the p-th exponential stability is obtained. Finally, an example is given to illustrate the availability of the obtained results.

scholarly journals On the approximations of solutions to stochastic differential equations under polynomial condition

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 11-25
Author(s):  
Dusan Djordjevic ◽  
Miljana Jovanovic
Keyword(s):  
Differential Equations ◽  
Theoretical Result ◽  
Stochastic Differential Equations ◽  
Approximate Method ◽  
Linear Growth ◽  
Growth Conditions ◽  
Time Interval ◽  
Initial Equation ◽  
The Subject ◽  
Approximate Equations

The subject of this paper is an analytic approximate method for a class of stochastic differential equations with coefficients that do not necessarily satisfy the Lipschitz and linear growth conditions but behave like a polynomials. More precisely, equations from the observed class have unique solutions with bounded moments and their coefficients satisfy polynomial condition. Approximate equations are defined on partitions of a time interval, and their coefficients are Taylor approximations of the coefficients of the initial equation. The rate of Lp convergence increases when degrees in Taylor approximations of coefficients increase. At the end of the paper, an example is provided to support the main theoretical result.

REFLECTED BSDES WITH STOCHASTIC MONOTONE GENERATOR AND APPLICATION TO VALUING AMERICAN OPTIONS

2020 ◽  
Vol 23 (05) ◽  
pp. 2050034
Author(s):  
MOHAMED MARZOUGUE
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
American Options ◽  
Growth Conditions ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Monotonicity ◽  
Uniqueness Of The Solution ◽  
Fair Valuation ◽  
Reflected Bsdes

In this paper, we prove the existence and uniqueness of the solution to backward stochastic differential equations with lower reflecting barrier in a Brownian setting under stochastic monotonicity and general increasing growth conditions. As an application, we study the fair valuation of American options.

scholarly journals Reflected backward stochastic differential equations under monotonicity and general increasing growth conditions

2005 ◽  
Vol 37 (1) ◽  
pp. 134-159 ◽  
Author(s):  
J.-P. Lepeltier ◽  
A. Matoussi ◽  
M. Xu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Growth Conditions ◽  
Backward Stochastic Differential Equations ◽  
Contingent Claim ◽  
Terminal Time ◽  
Uniqueness Of The Solution ◽  
American Contingent Claim

We prove the existence and uniqueness of the solution to certain reflected backward stochastic differential equations (RBSDEs) with one continuous barrier and deterministic terminal time, under monotonicity, and general increasing growth conditions on the associated coefficient. As an application, we obtain, in some constraint cases, the price of an American contingent claim as the unique solution of such an RBSDE.

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