SUCCESSIVE APPROXIMATIONS OF INFINITE DIMENSIONAL SDES WITH JUMP

2005 ◽  
Vol 05 (04) ◽  
pp. 609-619 ◽  
Author(s):  
GUILAN CAO ◽  
KAI HE ◽  
XICHENG ZHANG
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Infinite Dimensional

In this paper, we study the existence and uniqueness of solutions to non-Markovian stochastic differential equations with jump and non-Lipschitz coefficients in infinite dimensional spaces by successive approximation.

scholarly journals Prevalence of backward stochastic differential equations with unique solution

2004 ◽  
Vol 2004 (2) ◽  
pp. 123-136
Author(s):  
K. Bahlali ◽  
B. Mezerdi ◽  
Y. Ouknine
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Baire Category ◽  
Backward Stochastic Differential Equations ◽  
Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Almost All ◽  
Continuous Dependence Of Solutions

We prove that in the sense of Baire category, almost all backward stochastic differential equations (BSDEs) with bounded and continuous coefficient have the properties of existence and uniqueness of solutions as well as the continuous dependence of solutions on the coefficient and the L2-convergence of their associated successive approximations.

scholarly journals Existence and Uniqueness of Solutions for a Class of Nonlinear Stochastic Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Iryna Volodymyrivna Komashynska
Keyword(s):  
Differential Equations ◽  
Diffusion Process ◽  
Stochastic Differential Equations ◽  
Successive Approximation ◽  
Diffusion Coefficients ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Uniqueness Of Solutions ◽  
Nonlinear Stochastic Differential Equations

By using successive approximation, we prove existence and uniqueness result for a class of nonlinear stochastic differential equations. Moreover, it is shown that the solution of such equations is a diffusion process and its diffusion coefficients are found.

scholarly journals FILTERED STOCHASTIC CALCULUS

2001 ◽  
Vol 04 (03) ◽  
pp. 309-346 ◽  
Author(s):  
ROMUALD LENCZEWSKI
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Fock Space ◽  
Stochastic Calculus ◽  
Itô Formula ◽  
Uniqueness Of Solutions ◽  
Ito Formula ◽  
Itô Calculus ◽  
Boolean Independence

By introducing a color filtration to the multiplicity space [Formula: see text], we extend the quantum Itô calculus on multiple symmetric Fock space [Formula: see text] to the framework of filtered adapted biprocesses. In this new notion of adaptedness, "classical" time filtration makes the integrands similar to adapted processes, whereas "quantum" color filtration produces their deviations from adaptedness. An important feature of this calculus, which we call filtered stochastic calculus, is that it provides an explicit interpolation between the main types of calculi, regardless of the type of independence, including freeness, Boolean independence (more generally, m-freeness) as well as tensor independence. Moreover, it shows how boson calculus is "deformed" by other noncommutative notions of independence. The corresponding filtered Itô formula is derived. Existence and uniqueness of solutions of a class of stochastic differential equations are established and unitarity conditions are derived.

New inequalities of Gronwall type for the stochastic differential equations

2015 ◽  
Vol 23 (3) ◽  
Author(s):  
Mohamed-Ahmed Boudref ◽  
Ahmed Berboucha
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Inequalities ◽  
Uniqueness Of Solutions ◽  
Quantitative Properties ◽  
New Inequalities

AbstractIn this paper, we establish some new nonlinear integral inequalities of Gronwall type for Itô integrals. These inequalities generalize some inequalities which can be used in applications as handy tools to study the qualitative as well as quantitative properties of solutions of some stochastic differential equations. We will use this inequalities to show the existence and uniqueness of solutions for nonlinear EDS.

scholarly journals Random Fuzzy Differential Equations with Impulses

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ho Vu
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Picard Method

We consider the random fuzzy differential equations (RFDEs) with impulses. Using Picard method of successive approximations, we shall prove the existence and uniqueness of solutions to RFDEs with impulses under suitable conditions. Some of the properties of solution of RFDEs with impulses are studied. Finally, an example is presented to illustrate the results.

scholarly journals Successive Approximation Method of Integro–Differential Equation With Applications

2019 ◽  
Vol 8 (3) ◽  
pp. 96
Author(s):  
Samir H. Abbas ◽  
Younis M. Younis
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Differential Equations ◽  
Successive Approximation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximations ◽  
Successive Approximation Method ◽  
Integro Differential Equation

The aim of this paper is studying the existence and uniqueness solution of integro- differential equations by using Successive approximations method of picard. The results of written program in Mat-Lab show that the method is very interested and efficient with comparison the exact solution for solving of integro-differential equation.

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