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Stochastic Differential Equations and Integrating Factor
, 2013
"... Abstract The aim of this paper is the analytical solutions the family of firstorder nonlinear stochastic differential equations. We define an integrating factor for the large class of special nonlinear stochastic differential equations. With multiply both sides with the integrating factor, we intr ..."
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Abstract The aim of this paper is the analytical solutions the family of firstorder nonlinear stochastic differential equations. We define an integrating factor for the large class of special nonlinear stochastic differential equations. With multiply both sides with the integrating factor, we
Mutual information for stochastic differential equations
 Inform. Control
, 1971
"... Mutual information is calculated for processes described by stochastic differential equations. The expression for the mutual information has an interpretation in filtering theory. 1. ..."
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Cited by 2 (0 self)
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Mutual information is calculated for processes described by stochastic differential equations. The expression for the mutual information has an interpretation in filtering theory. 1.
Applied Stochastic Differential Equations
, 2012
"... The purpose of these notes is to provide an introduction to to stochastic differential equations (SDEs) from applied point of view. Because the aim is in applications, much more emphasis is put into solution methods than to analysis of the theoretical properties of the equations. From pedagogical po ..."
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The purpose of these notes is to provide an introduction to to stochastic differential equations (SDEs) from applied point of view. Because the aim is in applications, much more emphasis is put into solution methods than to analysis of the theoretical properties of the equations. From pedagogical
Modified equation for stochastic differential equation
, 2004
"... We describe a backward error analysis for stochastic differential equations with respect to weak convergence. Modified equations are provided for forward and backward Euler approximations to Itô SDEs with additive noise, and extensions to other types of equation and approximation are discussed. 1 ..."
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Cited by 15 (1 self)
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We describe a backward error analysis for stochastic differential equations with respect to weak convergence. Modified equations are provided for forward and backward Euler approximations to Itô SDEs with additive noise, and extensions to other types of equation and approximation are discussed. 1
Stability of Stochastic Differential Equations with Markovian Switching
, 1991
"... Stability of stochastic differential equations with Markovian switching has recently received a lot of attention. For example, stability of linear or semilinear type of such equations has been studied by Basak et al.[2], Ji & Chizeck [6] and Marlton [13]. The aim of this paper is to discuss the ..."
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Cited by 156 (45 self)
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Stability of stochastic differential equations with Markovian switching has recently received a lot of attention. For example, stability of linear or semilinear type of such equations has been studied by Basak et al.[2], Ji & Chizeck [6] and Marlton [13]. The aim of this paper is to discuss
SDELab: stochastic differential equations with MATLAB
, 2006
"... We introduce SDELab, a package for solving stochastic differential equations (SDEs) within MATLAB. SDELab features explicit and implicit integrators for a general class of Ito and Stratonovich SDEs, including Milstein's method, sophisticated algorithms for iterated stochastic integrals, and fle ..."
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Cited by 5 (0 self)
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We introduce SDELab, a package for solving stochastic differential equations (SDEs) within MATLAB. SDELab features explicit and implicit integrators for a general class of Ito and Stratonovich SDEs, including Milstein's method, sophisticated algorithms for iterated stochastic integrals
Stochastic differential equations with random coefficients
"... In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these ..."
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In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive
Numerical Solution of Stochastic Differential Equations
"... ABSTRACT: This paper provides an introduction to the main concepts and techniques necessary for someone who wishes to carryout numerical experiments involving Stochastic Differential Equation (SDEs). As SDEs are frictionless generally and the solutions are continuous stochastic process that represe ..."
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ABSTRACT: This paper provides an introduction to the main concepts and techniques necessary for someone who wishes to carryout numerical experiments involving Stochastic Differential Equation (SDEs). As SDEs are frictionless generally and the solutions are continuous stochastic process
On uniqueness of solutions to stochastic differential equations
, 2002
"... Abstract. We consider the stochastic differential equation dx(t) = dW(t) + f(t, x(t))dt, x(0) = x0 for t ≥ 0, where x(t) ∈ R d, W is a standard ddimensional Brownian motion, and f is a bounded Borel function from [0, ∞) × R d → R d to R d. We show that, for almost all Brownian paths W(t), there ..."
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Cited by 18 (0 self)
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Abstract. We consider the stochastic differential equation dx(t) = dW(t) + f(t, x(t))dt, x(0) = x0 for t ≥ 0, where x(t) ∈ R d, W is a standard ddimensional Brownian motion, and f is a bounded Borel function from [0, ∞) × R d → R d to R d. We show that, for almost all Brownian paths W
Results 11  20
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46,624