We give a causal interpretation of stochastic differential equations (SDEs) by defining the postintervention SDE resulting from an intervention in an SDE. We show that under Lipschitz conditions, the solution to the postintervention SDE is equal to a uniform limit in probability of postintervention structural equation models based on the Euler scheme of the original SDE, thus relating our defin...

Modifications to a stochastic differential equation (SDE) approach for modeling single and two phase NAPL flow are proposed which are intended to allow SDE modeling of the motion of air bubbles in porous media. Bubble flow and channeling are discussed along with bubble sticking, bubble coalescing, bubble breakup and air sparging.

For a certain scalar linear jump-diffusion stochastic differential equation (jump SDE) the asymptotic stability (i.e. convergence to zero as time t → ∞) is considered. Using the jump SDE as a test equation, two types of ‘balanced’ numerical methods are evaluated with respect to computational stability. For both methods it is shown by an analysis that for sufficiently small time steps the numeri...

We consider a stochastic differential equation (SDE) with piecewise linear drift driven by a spectrally one-sided Lévy process. We show that this SDE has some connections with queueing and storage models, and we use this observation to obtain the invariant distribution.

In this article, we prove that the inverse of the Malliavin matrix belongs to L(Ω,P) for a class of degenerate stochastic differential equation(SDE). The conditions required are similar to Hörmander’s bracket condition, but we don’t need all coefficients of the SDE are smooth. Furthermore, we obtain a locally uniform estimate for the Malliavin matrix and a gradient estimate. We also prove that ...

We consider the problem of estimating a nonlinear state-space model whose state process is driven by an ordinary differential equation (ODE) or a stochastic differential equation (SDE), with discrete-time data. We propose a new estimation method by minimizing the conditional least squares (CLS) with the conditional mean function computed approximately via unscented Kalman filter (UKF). We deriv...

We present a systematic formalism to derive a path-integral formulation for hard-core particle systems far from equilibrium. Writing the master equation for a stochastic process of the system in terms of the annihilation and creation operators with mixed commutation relations, we find the Kramers-Moyal coefficients for the corresponding Fokker-Planck equation (FPE), and the stochastic different...

In this paper, we present a scheme of stochastic hybrid system which introduces randomness to the deterministic framework of the traditional hybrid systems by allowing the flow inside each invariant set of the discrete state variables to be governed by stochastic differential equation (SDE) rather than the deterministic ones. The notion of embedded Markov chains is proposed for such systems and...

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with earlier proposed model of tra...

We explain how Itô Stochastic Differential Equations on manifolds may be defined as 2-jets of curves. We use jets as a natural language to express geometric properties of SDEs and show how jets can lead to intuitive representations of Itô SDEs, including three different types of drawings. We explain that the mainstream choice of Fisk-StratonovichMcShane calculus for stochastic differential geom...