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.

Well-posedness of Stratonovich multi-valued SDEs driven by semimartingales

2014 ◽  
Vol 14 (04) ◽  
pp. 1450005
Author(s):  
Jing Wu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Time Change ◽  
Random Time ◽  
Approximation Technique ◽  
Well Posedness ◽  
Uniqueness Of Solutions ◽  
Random Time Change

In this paper we consider Stratonovich type multi-valued stochastic differential equations (MSDEs) driven by general semimartingales. Based on an existence and uniqueness result for MSDEs with respect to continuous semimartingales, we apply the random time change and approximation technique to prove existence and uniqueness of solutions to Stratonovich type multi-valued SDEs driven by general semimartingales with summable jumps.

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.

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

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 Some Existence Results for Systems of Impulsive Stochastic Differential Equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sliman Mekki ◽  
Tayeb Blouhi ◽  
Juan J. Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Impulsive Systems ◽  
Uniqueness Of Solutions

Abstract In this paper we study a class of impulsive systems of stochastic differential equations with infinite Brownian motions. Sufficient conditions for the existence and uniqueness of solutions are established by mean of some fixed point theorems in vector Banach spaces. An example is provided to illustrate the theory.

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