In this paper, the existence and uniqueness theorem of fuzzy stochastic ordinary differential equations, based on the mean square convergence of the mathematical induction approximations to the associated stochastic integral equation, are stated and demonstrated.Kareem, Nabaa R....
Stochastic differential equationsStochastic ordinary differential equations may have solutions that explode in finite time. In this article we prove the continuity of the explosion time with respect to the different parameters appearing in the equation, such as the initial datum, the drift, and the ...
In this paper, we show that the integration of a stochastic differential equation driven by G-Brownian motion (G-SDE for short) in R can be reduced to the integration of an ordinary differential equation (ODE for short) parameterized by a variable in (Ω,F). By this result, we obtain ...
we give three Runge-Kutta numerical schemes for stochastic ordinary differential equations: explicit scheme,semi-implicit scheme and implicit scheme.The conditions of T-stability for the three Runge-Kutta numerical schemes are discussed and partial numerical results for a test linear equation are shown....
The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems ode dde partial-differential-equations differential-equations ordinary-differential-equations differentialequations sde pde dae stochastic-differential-equations delay-...
An SDE is essentially a classical differential equation which is perturbed by a random noise. When nothing else is specified, SDE means in fact ordinary SDE; in that case it corresponds to the perturbation of an ordinary differential equation. Stochastic partial differential equations (SPDEs) are ...
90 5. STOCHASTIC DIFFERENTIAL EQUATIONS PROOF. The stochastic differential equation looks very much like an or- dinary differential equation: dx t = b(x t ) dt. In fact this is a special case of the general stochastic differential equation formulated above. Recall that ordinary differential equa...
The pioneering work of Runge and Kutta a hundred years ago has ultimately led to suites of sophisticated numerical methods suitable for solving complex systems of deterministic ordinary differential equations. However, in many modelling situations, the appropriate representation is a stochastic differential...
THE NUMERICAL STABILITY OF STOCHASTIC ORDINARY DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE. An asymptotic stability analysis of numerical methods used for simulating stochastic differential equations with additive noise is presented. The initial p... BUCKWAR,E.,RIEDLER,... - 《Stochastics & Dynamics》 被...
19 Stochastic differential equationsThe ordinary differential equation𝑑𝑑𝑠𝑥𝑠= 𝑏(𝑠,𝑥𝑠),𝑥(0) = 𝑥0, describes the position𝑥𝑡of a particle which moves with speed𝑏(𝑠,𝑥)depending on time and on the currentposition. One possibility to take into account random...