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Stochastic Processes and their Applications, ISSN 0304-4149, 12/2019, Volume 129, Issue 12, pp. 4926 - 4964
For backward stochastic Volterra integral equations (BSVIEs, for short), under some mild conditions, the so-called adapted solutions or adapted M-solutions... 
Representation of adapted solutions | Backward stochastic Volterra integral equations | Adapted solutions | Representation partial differential equations | SCHEME | THEOREMS | DIFFERENTIAL-EQUATIONS | SDES | STATISTICS & PROBABILITY | WELL-POSEDNESS | Differential equations
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 03/2018, Volume 330, pp. 574 - 585
In this study, a practical matrix method based on operational matrices of integration and collocation points is presented to find the approximate solution of... 
Brownian motion process | Stochastic Itô–Volterra integral equations | Error analysis | Euler polynomials | Stochastic operational matrix | SYSTEM | MATHEMATICS, APPLIED | OPERATIONAL MATRICES | COEFFICIENTS | COMPUTATIONAL METHOD | BERNOULLI | FREDHOLM INTEGRODIFFERENTIAL EQUATIONS | Stochastic Ito-Volterra integral equations
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2017, Volume 317, pp. 447 - 457
The Euler–Maruyama method is presented for linear stochastic Volterra integral equations. Then the strong convergence property is analyzed for convolution... 
Strong convergence | Stochastic | The Euler–Maruyama method | Strong superconvergence | Volterra integral equations | ORDER | MATHEMATICS, APPLIED | EXPONENTIAL STABILITY | The Euler-Maruyama method | COMPUTATIONAL METHOD | CONVERGENCE | DELAY | Analysis | Methods | Differential equations
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 08/2013, Volume 219, Issue 24, pp. 11278 - 11290
We consider fuzzy stochastic integral equations with stochastic Lebesgue trajectory integrals and fuzzy stochastic Itô trajectory integrals. Some methods of... 
Stochastic fuzzy differential equation | Uncertainty | Approximate solution | Fuzzy stochastic trajectory integral | Fuzzy stochastic integral equation | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | ITO TYPE | Fuzzy logic | Approximation | Integral equations | Mathematical analysis | Mathematical models | Fuzzy set theory | Stochasticity | Fuzzy
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 05/2018, Volume 333, pp. 74 - 86
The main aim of this study is to propose a numerical iterative approach for obtaining approximate solutions of nonlinear stochastic Itô –Volterra integral... 
Stochastic Volterra integral equations | Brownian motion process | Itô integral | Linear spline interpolation | Successive approximations method | Ito integral | OPERATIONAL MATRIX | MATHEMATICS, APPLIED | GALERKIN METHOD | COMPUTATIONAL METHOD
Journal Article
2005, Mathematical and analytical techniques with applications to engineering, ISBN 9780387251752, xx, 434
Derivation of Ito's formulas, Girsanov's theorems and martingale representation theorem for stochastic DEs with jumpsApplications to population... 
Stochastic differential equations | Mathematics | Engineering | Engineering Fluid Dynamics | Applications of Mathematics | Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Financial Economics
Book
Stochastic Processes and their Applications, ISSN 0304-4149, 02/2019, Volume 129, Issue 2, pp. 626 - 633
We present an explicit solution triplet (Y,Z,K) to the backward stochastic Volterra integral equation (BSVIE) of linear type, driven by a Brownian motion and a... 
Brownian motion | Compensated Poisson random measure | Linear equation | Hida–Malliavin derivative | Explicit solution | Volterra type backward stochastic differential equation | Hida-Malliavin derivative | STATISTICS & PROBABILITY
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 11/2014, Volume 247, pp. 1011 - 1020
A numerical method for solving nonlinear Stochastic Itô–Volterra equations is proposed. The method is based on delta function (DF) approximations. The... 
Delta functions | Error analysis | Stochastic | Collocation | Vector forms | Operational matrices | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | RANDOM DIFFERENTIAL-EQUATIONS | INTEGRODIFFERENTIAL EQUATIONS | Approximation | Computation | Mathematical analysis | Nonlinearity | Mathematical models | Stochasticity | Dynamical systems | Delta function
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 03/2020, Volume 79, Issue 5, pp. 1435 - 1446
This paper aims to study a new class of integral equations called backward doubly stochastic Volterra integral equations (BDSVIEs, for short). The notion of... 
Symmetrical martingale solution | Backward stochastic integral | Backward doubly stochastic Volterra integral equation
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 08/2020, Volume 54, p. 103104
We prove some existence and uniqueness results for a nonlinear stochastic integral equation using fixed-point theory methods to ensure the convergence of the... 
Integral equation | Renormalization of Banach space | Stochastic equation | Fixed point methods
Journal Article
2013, ISBN 9789814447997, xiii, 159
Book
2005, ISBN 0521850150, x, 381
This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability theory. The basic... 
Measure theory | Integrals | Martingales (Mathematics) | Mathematics
Book