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Numerical Integration of Stochastic Differential Equations
Bell System Technical Journal, 1979In a previous paper, a method was presented to integrate numerically nonlinear stochastic differential equations (SDEs) with additive, Gaussian, white noise. The method, a generalization of the Range Kutta algorithm, extrapolates from one point to the next applying functional evaluations at stochastically determined points.
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INTEGRATION OF STOCHASTIC DIFFERENTIAL EQUATIONS ON A COMPUTER
International Journal of Modern Physics C, 2002A brief introduction to the simulation of stochastic differential equations is presented. Algorithms to simulate rare fluctuations, a topic of interest in the light of recent theoretical work on optimal paths are studied. Problems connected to the treatment of the boundaries and correlated noise will also be discussed.
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A New Representation for Stochastic Integrals and Equations
SIAM Journal on Control, 1966zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ISDEP: Integrator of stochastic differential equations for plasmas
Computer Physics Communications, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jose Luis Velasco +5 more
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Stochastic multisymplectic integrator for stochastic KdV equation
AIP Conference Proceedings, 2012In this paper we investigate the stochastic multisymplectic methods to solve the stochastic partial differential equation. The stochastic KdV equations are considered. Besides conserving the multi-symplectic structure of original equation, the stochastic multi-symplectic methods are also investigated for the conservation of various conservation laws ...
Shanshan Jiang, Lijin Wang, Jialin Hong
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On set-valued stochastic integrals and fuzzy stochastic equations
Fuzzy Sets and Systems, 2011The author establishes the notion of a set-valued trajectory stochastic integral in a semimartingale framework. The notion of this set-valued stochastic integral arises in a natural way by the corresponding notion of the decomposable hull of a map with respect to a semimartingale and a filtration. Formal stochastic equations are studied with respect to
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Manipulating Stochastic Differential Equations and Stochastic Integrals
2015Many of the calculations of derivative security pricing involve formal manipulations of stochastic differential equations and stochastic integrals. This chapter derives those that are most frequently used. We also consider transformation of correlated Wiener processes to uncorrelated Wiener processes for higher dimensional stochastic differential ...
Carl Chiarella +2 more
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Equations for stochastic path integrals
Mathematical Proceedings of the Cambridge Philosophical Society, 1961Apart from the study of the integralwhere {X(u)} is a stationary Gaussian process with autocorrelation function ρ(t), by Kac and Siegert(1), most stochastic functionals of the general typehave been considered for {X(u)} either additive or Markovian (see, for example, (2), (3)), and in the Markovian case only for diffusion-type processes (Darling and ...
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