Using a stochastic differential equation (SDE) approach, we examine the dynamics of the continental-scale water balance in the central United States. Whitenoise and colored-noise versions of the model are developed based on analysis of atmospheric data from the National Center for Environmental Prediction (NCEP) reanalysis project and long-term records of precipitation and soil moisture. Improv...

This paper introduces a new approach of approximate Bayesian inference for Stochastic Differential Equation (SDE) models. This approach is not MCMC based and aims to provide a more efficient option for Bayesian inference on SDE models. There are two novel aspects about this approach: the first concerns the way in which the parameter space is explored and the second concerns the evaluation of th...

This paper is mainly concerned with whether the almost sure exponential stability of stochastic differential equations (SDEs) is shared with that of a numerical method. Under the global Lipschitz condition, we first show that the SDE is pth moment exponentially stable (for p ∈ (0, 1)) if and only if the stochastic theta method is pth moment exponentially stable for a sufficiently small step siz...

in this paper, we propose a new method for solving the stochastic advection-diffusion equation of ito type. in this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit milstein scheme for the resulting linear stochastic system of differential equation. the main purpose of this paper is the stability investigatio...

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...

We consider a bidimensional Ornstein-Uhlenbeck process to describe the tissue microvascularisation in anti-cancer therapy. Data are discrete, partial and noisy observations of this stochastic differential equation (SDE). Our aim is the estimation of the SDE parameters. We use the main advantage of a one-dimensional observation to obtain an easy way to compute the exact likelihood using the Kalm...

Metropolized integrators for ergodic stochastic differential equations (SDE) are proposed which (i) are ergodic with respect to the (known) equilibrium distribution of the SDE and (ii) approximate pathwise the solutions of the SDE on finite time intervals. Both these properties are demonstrated in the paper and precise strong error estimates are obtained. It is also shown that the Metropolized ...

We propose a linear-quadratic (LQ) control problem of streamflow discharge by optimizing an infinite-dimensional jump-driven stochastic differential equation (SDE). Our SDE is superposition Ornstein-Uhlenbeck processes (supOU process), generating sub-exponential autocorrelation function observed in actual data. The integral operator Riccati heuristically derived to determine the optimal system....

Non-parametric modeling is a method which relies heavily on data and motivated by the smoothness properties in estimating a function which involves spline and non-spline approaches. Spline approach consists of regression spline and smoothing spline. Regression spline with Bayesian approach is considered in the first step of a two-step method in estimating the structural parameters for stochasti...

Stochastic differential equation (SDE) models have shown useful to describe continuous time processes, e.g. a physiological process evolving in an individual. Biomedical experiments often imply repeated measurements on a series of individuals or experimental units and individual differences can be represented by incorporating random effects into the model. When both system noise and individual ...