Bounded solutions for general time interval BSDEs with quadratic growth coefficients and stochastic conditions

2018 ◽  
Vol 18 (05) ◽  
pp. 1850034
Author(s):  
Huan-Huan Luo ◽  
Sheng-Jun Fan
Keyword(s):  
Differential Equations ◽  
Finite Time ◽  
Quadratic Growth ◽  
Time Interval ◽  
Finite Time Interval ◽  
Bounded Solutions ◽  
One Dimensional ◽  
Stochastic Conditions ◽  
New Ideas ◽  
General Time

This paper deals with bounded solutions for general time interval one-dimensional backward stochastic differential equations (BSDEs for short) with quadratic growth coefficients and stochastic conditions. Several general results of existence, uniqueness, stability and comparison for the bounded solutions are put forward and established, which improve considerably some existing works, even though for the case of finite time interval. Some new ideas are also developed to establish these results.

A method for approximating the probability functions of a Markov chain

1988 ◽  
Vol 25 (4) ◽  
pp. 808-814 ◽  
Author(s):  
Keith N. Crank
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Finite Number ◽  
Continuous Time ◽  
Finite Time ◽  
The State ◽  
Time Interval ◽  
Continuous Time Markov Chain ◽  
Finite Time Interval ◽  
System Of Differential Equations

This paper presents a method of approximating the state probabilities for a continuous-time Markov chain. This is done by constructing a right-shift process and then solving the Kolmogorov system of differential equations recursively. By solving a finite number of the differential equations, it is possible to obtain the state probabilities to any degree of accuracy over any finite time interval.

Co-jumps

2014 ◽  
Author(s):  
Yacine Aïıt-Sahalia ◽  
Jean Jacod
Keyword(s):  
Finite Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
Underlying Process ◽  
One Dimensional ◽  
Observation Times

This chapter considers some questions which only make sense in a multivariate setting. It deals with two problems: one is about a multidimensional underlying process X, and we want to decide whether two particular components of X jump at the same time: this can happen always, or never, or for some but not all jump times. The second problem is again about a one-dimensional underlying process X, but we study the pair (X, σ‎), with the second component being the volatility of the first component X. Again, we want to decide whether X and σ‎ jump at the same times, always, or never, or sometimes. The process X is observed at the regularly spaced observation times iΔ‎₀, within a finite time interval [0, T].

scholarly journals Parameter Estimation of Sigmoid Superpositions: Dynamical System Approach

2003 ◽  
Vol 15 (10) ◽  
pp. 2419-2455 ◽  
Author(s):  
Ivan Tyukin ◽  
Cees van Leeuwen ◽  
Danil Prokhorov
Keyword(s):  
Dynamical System ◽  
Parameter Estimation ◽  
Differential Equations ◽  
Linear Combination ◽  
Finite Time ◽  
System Approach ◽  
Effective Procedure ◽  
Time Interval ◽  
Sigmoid Function ◽  
Finite Time Interval

Superposition of sigmoid function over a finite time interval is shown to be equivalent to the linear combination of the solutions of a linearly parameterized system of logistic differential equations. Due to the linearity with respect to the parameters of the system, it is possible to design an effective procedure for parameter adjustment. Stability properties of this procedure are analyzed.

STABILITY ANALYSIS OF DIFFERENTIAL EQUATIONS WITH TIME-DEPENDENT DELAY

2006 ◽  
Vol 16 (02) ◽  
pp. 465-472 ◽  
Author(s):  
WEIHUA DENG ◽  
YUJIANG WU ◽  
CHANGPIN LI
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Finite Time ◽  
Time Dependent ◽  
Time Interval ◽  
Finite Time Interval ◽  
Predator Prey ◽  
Gauss Type ◽  
Predator Prey Models ◽  
The Stability

In this Letter, we study the stability of differential equations with time-dependent delay. Several theorems are established for stability on a finite time interval, called "interval stability" for simplicity, and Liapunov stability. These theorems are applied to the generalized Gauss-type predator–prey models, and satisfactory results are obtained.

scholarly journals Application of the averaging method to the problems of optimal control of the impulse systems

2020 ◽  
Vol 12 (2) ◽  
pp. 504-521
Author(s):  
T.V. Koval'chuk ◽  
V.V. Mogylova ◽  
O.M. Stanzhytskyi ◽  
T.V. Shovkoplyas
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Finite Time ◽  
Averaging Method ◽  
Optimal Synthesis ◽  
Time Interval ◽  
Finite Time Interval ◽  
System Of Differential Equations ◽  
Existence Of Optimal Control

The problem of optimal control at finite time interval for a system of differential equations with impulse action at fixed moments of time as well as the corresponding averaged system of ordinary differential equations are considered. It is proved the existence of optimal control of exact and averaged problems. Also, it is established that optimal control of averaged problem realize the approximate optimal synthesis of exact problem. The main result of the article is a theorem, where it is proved that optimal contol of an averaged problem is almost optimal for exact problem. Substantiation of proximity of solutions of exact and averaged problems is obtained.

A method for approximating the probability functions of a Markov chain

1988 ◽  
Vol 25 (04) ◽  
pp. 808-814 ◽  
Author(s):  
Keith N. Crank
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Finite Number ◽  
Continuous Time ◽  
Finite Time ◽  
The State ◽  
Time Interval ◽  
Continuous Time Markov Chain ◽  
Finite Time Interval ◽  
System Of Differential Equations

This paper presents a method of approximating the state probabilities for a continuous-time Markov chain. This is done by constructing a right-shift process and then solving the Kolmogorov system of differential equations recursively. By solving a finite number of the differential equations, it is possible to obtain the state probabilities to any degree of accuracy over any finite time interval.

scholarly journals The enclosure method for inverse obstacle scattering over a finite time interval: IV. Extraction from a single point on the graph of the response operator

2017 ◽  
Vol 25 (6) ◽  
Author(s):  
Masaru Ikehata
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Finite Time ◽  
Single Point ◽  
Obstacle Problems ◽  
Time Interval ◽  
Finite Time Interval ◽  
Partial Differential ◽  
Response Operator ◽  
Enclosure Method

AbstractA final and maybe the simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a

scholarly journals Regularization of inclusions of differential equations solutions based on the kinematics of a vector field in stability problems

2021 ◽  
Vol 2099 (1) ◽  
pp. 012045
Author(s):  
A N Rogalev
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Finite Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
Solution Sets ◽  
Strong Growth ◽  
System Parameters ◽  
The Stability

Abstract This paper presents the new results of computing the inclusions of sets of solutions of ordinary differential equations corresponding to perturbations acting on the solutions of the system. The regularization of algorithms for the inclusion of solutions is investigated. Inclusions of solutions are used to study the stability over a finite time interval under perturbations of the system parameters. The boundaries of solutions sets using methods that construct symbolic formulas that characterize the behavior of the system are computed. In this case, the Influence of permanent disturbances on the solutions is taken into account. It is proposed to use the parameters of the vector field of the problem in order to compensate for a strong growth of the computable solution boundaries, which is often encountered in many methods. This means the regularization of the problem of estimating inclusions of solution sets.

scholarly journals Stability of Nonlinear Systems of Fractional Order Differential Equations

2010 ◽  
Vol 7 (4) ◽  
pp. 1458-1461
Author(s):  
Baghdad Science Journal
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Fractional Order ◽  
Finite Time ◽  
Time Interval ◽  
Sufficient Condition ◽  
Finite Time Interval ◽  
Infinite Time ◽  
Fractional Order Differential Equations ◽  
Infinite Time Interval

In this paper, a sufficient condition for stability of a system of nonlinear multi-fractional order differential equations on a finite time interval with an illustrative example, has been presented to demonstrate our result. Also, an idea to extend our result on such system on an infinite time interval is suggested.

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