Existence Results For Some Second-Order Stochastic Differential Equations

2011 ◽  
pp. 197-212
Author(s):  
Paul H. Bezandry ◽  
Toka Diagana
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence Results ◽  
Second Order

scholarly journals Infinite Boundary Value Problems for Second-Order Nonlinear Impulsive Differential Equations with Supremum

2010 ◽  
Vol 2010 ◽  
pp. 1-15
Author(s):  
Piao-Piao Shi ◽  
Wen-Xia Wang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Solution Method ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Existence Results ◽  
Second Order ◽  
Comparison Result ◽  
Upper Solution ◽  
Lower And Upper Solution

We investigate the infinite boundary value problems for second-order impulsive differential equations with supremum by establishing a new comparison result and using the lower and upper solution method, and obtain the existence results for their maximal and minimal solutions.

scholarly journals Existence results for differential equations with reflection of the argument

1994 ◽  
Vol 57 (2) ◽  
pp. 237-260 ◽  
Author(s):  
Donal O'Regan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence Results ◽  
Second Order ◽  
Systems Of Differential Equations ◽  
Nonlinear Alternative ◽  
Point Analysis ◽  
Second Order Equations

AbstractExistence principles are given for systems of differential equations with reflection of the argument. These are derived using fixed point analysis, specifically the Nonlinear Alternative. Then existence results are deduced for certain classes of first and second order equations with reflection of the argument.

A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus

2019 ◽  
Vol 25 (4) ◽  
pp. 341-361
Author(s):  
Riu Naito ◽  
Toshihiro Yamada
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Differential Equations ◽  
Least Squares ◽  
Stochastic Differential Equations ◽  
Malliavin Calculus ◽  
Second Order ◽  
Discretization Method ◽  
Local Approximations ◽  
Backward Sdes

Abstract The paper proposes a new second-order discretization method for forward-backward stochastic differential equations. The method is given by an algorithm with polynomials of Brownian motions where the local approximations using Malliavin calculus play a role. For the implementation, we introduce a new least squares Monte Carlo method for the scheme. A numerical example is illustrated to check the effectiveness.

Boundary value problems on noncompact intervals

1995 ◽  
Vol 125 (4) ◽  
pp. 777-799 ◽  
Author(s):  
Donal O'Regan
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Existence Results ◽  
Second Order

Existence results are established for second-order boundary value problems for ordinary differential equations on non-compact intervals.

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