The temporal autocorrelation (AC) function associated with monitoring order parameters characterizing conformational fluctuations of an enzyme is analyzed using a collection of surrogate models. The surrogates considered are phenomenological stochastic differential equation (SDE) models. It is demonstrated how an ensemble of such surrogate models, each surrogate being calibrated from a single t...

The time evolution of the value of a firm is commonly modeled by a linear, scalar stochastic differential equation (SDE) of the type   d d d t t t v t V rV t t V W      v t  d t r v is where the coefficient in the drift term denotes the (exogenous) stochastic short term interest rate and is the given volatility of the value process. In turn, the dynamics of the short term interest rate,...

Stochastic Differential Equation (SDE) models are used to describe the dynamics of complex systems with inherent randomness. The primary purpose of these models is to study rare but interesting or important behaviours, such as the formation of a tumour. Stochastic simulations are the most common means for estimating (or bounding) the probability of rare behaviours, but the cost of simulations i...

In this paper we study solutions to stochastic differential equations (SDEs) with discontinuous drift. We apply two approaches: The Euler-Maruyama method and the Fokker-Planck equation and show that a candidate density function based on the Euler-Maruyama method approximates a candidate density function based on the stationary Fokker-Planck equation. Furthermore, we introduce a smooth function ...

In this paper, we consider the problem of Bayesian filtering and inference for time series data modeled as noisy, discrete-time observations of a stochastic differential equation (SDE) with undetermined parameters. We develop a Metropolis algorithm to sample from the high-dimensional joint posterior density of all SDE parameters and state time series. Our approach relies on an innovative densit...

Software testing is a process to detect the errors in a totality and worth of developed software. Software reliability models provide quantitative measures of the software development processes. In this paper, an attempt has been made to discuss some testing domain based software reliability models and testing software and testing domain software reliability models based on ItO types Stochastic...

We consider a nonlinear differential equation under the combined influence of small state-dependent Brownian perturbations size ε, and fast periodic sampling with period δ; 0<ε,δ≪1. State samples (measurements) are taken every δ time units, instantaneous rate change state depends on both current value most recent sample. For resulting stochastic process indexed by ε,δ, we obtain asymptotic appr...

Fix a filtered probability space (S~, ,~, P) and a Brownian motion B on that space and consider any solution process X (on Q) to a stochastic differential equation (SDE) dXt = f (t, X) dBt + g(t, X ) dt (1). A well-known theorem states that pathwise uniqueness implies that the solution X to SDE (1) is strong, i.e., it is adapted to the P-completed filtration generated by B. Pathwise uniqueness ...

A Milstein-type scheme was proposed to improve the rate of convergence of its approximation of the solution to a stochastic differential equation driven by a vector of continuous semimartingales. A necessary and sufficient condition was provided for this rate to be 1/n when the SDE is driven by a vector of continuous local martingales, or continuous semimartingales under an additional assumptio...

We present an introduction to phase-space techniques ~PST! based on a quantum-field-theoretical ~QFT! approach. In addition to bridging the gap between PST and QFT, our approach results in a number of generalizations of the PST. First, for problems where the usual PST do not result in a genuine Fokker-Planck equation ~even after phase-space doubling! and hence fail to produce a stochastic diffe...