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39,985
USER’S GUIDE TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
, 1992
"... The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking argume ..."
Abstract
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Cited by 1399 (16 self)
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The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking
The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations
- SIAM J. SCI. COMPUT
, 2002
"... We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dime ..."
Abstract
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Cited by 398 (42 self)
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We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces
Analysis of Fractional Differential Equations
, 1999
"... We discuss existence, uniqueness and structural stability of solutions of nonlinear dierential equations of fractional order. The dierential operators are taken in the Riemann-Liouville sense and the initial conditions are specied according to Caputo's suggestion, thus allowing for interpretati ..."
Abstract
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Cited by 205 (4 self)
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We discuss existence, uniqueness and structural stability of solutions of nonlinear dierential equations of fractional order. The dierential operators are taken in the Riemann-Liouville sense and the initial conditions are specied according to Caputo's suggestion, thus allowing
Numerical Integration of Stochastic Differential Equations
, 1995
"... Abstract. We propose a new concept which allows us to apply any numerical method of weak approximation to a very broad class of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients. Following this concept, we discard the approximate trajectories which leave a sufficiently ..."
Abstract
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Cited by 200 (12 self)
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Abstract. We propose a new concept which allows us to apply any numerical method of weak approximation to a very broad class of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients. Following this concept, we discard the approximate trajectories which leave a
Mean-field backward stochastic differential equations and related patial differential equations
, 2007
"... In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward SDEs, corresponding to a large number of “particles” (or “a ..."
Abstract
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Cited by 181 (14 self)
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In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward SDEs, corresponding to a large number of “particles” (or
DIFFERENTIAL EQUATIONS
"... The geometric approach to the study of differential equations goes back to Sophus Lie and Elie Cartan. According to the modern inter-pretation of this approach, based on the notion ofjet space, we consider a differential equation as a submanifold in the jet space with induced geometric structure. Us ..."
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The geometric approach to the study of differential equations goes back to Sophus Lie and Elie Cartan. According to the modern inter-pretation of this approach, based on the notion ofjet space, we consider a differential equation as a submanifold in the jet space with induced geometric structure
Results 1 - 10
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39,985
