On the stopping time problem of interval-valued differential equations under generalized Hukuhara differentiability

2021 ◽  
Author(s):  
Hongzhou Wang ◽  
Rosana Rodríguez-López ◽  
Alireza Khastan
Keyword(s):  
Differential Equations ◽  
Stopping Time ◽  
Time Problem ◽  
Generalized Hukuhara Differentiability ◽  
Interval Valued

The continuous-time problem with interval-valued functions: applications to economic equilibrium

2018 ◽  
Vol 34 (6) ◽  
pp. 1123-1144
Author(s):  
G. Ruiz-Garzón ◽  
R. Osuna-Gómez ◽  
A. Rufián-Lizana ◽  
Y. Chalco-Cano
Keyword(s):  
Continuous Time ◽  
Economic Equilibrium ◽  
Time Problem ◽  
Interval Valued

scholarly journals Fuzzy Volterra Integro-Differential Equations Using General Linear Method

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 381 ◽  
Author(s):  
Zanariah Abdul Majid ◽  
Faranak Rabiei ◽  
Fatin Abd Hamid ◽  
Fudziah Ismail
Keyword(s):  
Differential Equations ◽  
Lagrange Interpolation ◽  
Linear Method ◽  
Interpolation Polynomial ◽  
General Linear ◽  
Kutta Method ◽  
Lagrange Interpolation Polynomial ◽  
Runge Kutta Method ◽  
General Linear Method ◽  
Generalized Hukuhara Differentiability

In this paper, a fuzzy general linear method of order three for solving fuzzy Volterra integro-differential equations of second kind is proposed. The general linear method is operated using the both internal stages of Runge-Kutta method and multivalues of a multisteps method. The derivation of general linear method is based on the theory of B-series and rooted trees. Here, the fuzzy general linear method using the approach of generalized Hukuhara differentiability and combination of composite Simpson’s rules together with Lagrange interpolation polynomial is constructed for numerical solution of fuzzy volterra integro-differential equations. To illustrate the performance of the method, the numerical results are compared with some existing numerical methods.

scholarly journals Undiscounted Markov Chain BSDEs to Stopping Times

2014 ◽  
Vol 51 (1) ◽  
pp. 262-281
Author(s):  
Samuel N. Cohen
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Continuous Time ◽  
Stopping Time ◽  
Stopping Times ◽  
Hitting Times ◽  
Continuous Time Markov Chain ◽  
Countable State ◽  
Growth Bound ◽  
Novel Applications

We consider backward stochastic differential equations in a setting where noise is generated by a countable state, continuous time Markov chain, and the terminal value is prescribed at a stopping time. We show that, given sufficient integrability of the stopping time and a growth bound on the terminal value and BSDE driver, these equations admit unique solutions satisfying the same growth bound (up to multiplication by a constant). This holds without assuming that the driver is monotone in y, that is, our results do not require that the terminal value be discounted at some uniform rate. We show that the conditions are satisfied for hitting times of states of the chain, and hence present some novel applications of the theory of these BSDEs.

Sign in / Sign up

Export Citation Format

Share Document