scholarly journals Existence Theorems for Solutions to Set-Valued Stochastic Differential Equations and Applications

2012 ◽  
Vol 1 ◽  
pp. 1-15
Author(s):  
Vu Ho ◽  
Van Hoa Ngo
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Wiener Process ◽  
Langevin Equation ◽  
Stock Prices ◽  
Hausdorff Space ◽  
Existence Theorems ◽  
Uniqueness Of Solution ◽  
Hukuhara Derivative ◽  
Interval Valued

In this paper, a class of new stochastic differential equations on semilinear Hausdorff space under Hukuhara derivative, called set-valued stochastic differential equations (SSDEs) driven by a Wiener process. Moreover, some corresponding properties of SSDEs are discussed such as existence, uniqueness of solution. Finaly, we give some applications to models of interval-valued stochastic differential equations such as stock prices model and the Langevin equation.

scholarly journals Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds

2021 ◽  
Author(s):  
Adrien Laurent ◽  
Gilles Vilmart
Keyword(s):  
Invariant Measure ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Linear Group ◽  
Langevin Equation ◽  
Numerical Experiments ◽  
Special Linear Group ◽  
Order Conditions ◽  
High Order ◽  
Differential Equations On Manifolds

AbstractWe derive a new methodology for the construction of high-order integrators for sampling the invariant measure of ergodic stochastic differential equations with dynamics constrained on a manifold. We obtain the order conditions for sampling the invariant measure for a class of Runge–Kutta methods applied to the constrained overdamped Langevin equation. The analysis is valid for arbitrarily high order and relies on an extension of the exotic aromatic Butcher-series formalism. To illustrate the methodology, a method of order two is introduced, and numerical experiments on the sphere, the torus and the special linear group confirm the theoretical findings.

scholarly journals Anticipated backward doubly stochastic differential equations with non-Liphschitz coefficients

2019 ◽  
Vol 4 (1) ◽  
pp. 9-20 ◽  
Author(s):  
Sadibou Aidara
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solution ◽  
Doubly Stochastic ◽  
New Type

AbstractIn this work, we deal with a new type of differential equations called anticipated backward doubly stochastic differential equations. We establish existence and uniqueness of solution in the case of non-Lipschitz coefficients.

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