The simulation of ion-channel noise has an important role in computational neuroscience. In recent years several approximate methods of carrying out this simulation have been published, based on stochastic differential equations, and all giving slightly different results. The obvious, and essential, question is: which method is the most accurate and which is most computationally efficient? Here...

It is shown that for an SDE in a Hilbert space, eventual compactness of the driving semigroup together with compact perturbations can be used to establish the existence of an invariant measure. The result is applied to stochastic functional differential equations and the heat equation perturbed by delay and noise, which are both shown to be driven by an eventually compact semigroup.

This article is concerned with the design of a feedback control based on past states in order to make given unstable hybrid stochastic differential equation (SDE) be stable distribution (stabilization distribution). first this direction. Under global Lipschitz condition coefficients SDE, we will show that stabilization can achieved by linear delay controls. In particular, discuss how controls t...

We consider a continuous time model for election timing in a Majoritarian Parliamentary System where the government maintains a constitutional right to call an early election. Our model is based on the two-party-preferred data that measure the popularity of the government and the opposition over time. We describe the poll process by a Stochastic Differential Equation (SDE) and use a martingale ...

This paper presents a model for option pricing in markets that experience financial crashes. The stochastic differential equation (SDE) of stock price dynamics is coupled to a post-crash market index. The resultant SDE is shown to have stock price and time dependent volatility. The partial differential equation (PDE) for call prices is derived using risk-neutral pricing. European call prices ar...

We propose an unbiased Monte-Carlo estimator for E[g(X t1,,X tn)], where X is a diffusion process defined by a multi-dimensional stochastic differential equation (SDE). The main idea is to start instead from a well-chosen simulatable SDE whose coefficients are updated at independent exponential times. Such a simulatable process can be viewed as a regimeswitching SDE, or as a branching diffusion...

J.A. Ellison, U. New Mexico H. Mais, DESY G. Ripken, Deceased 2004 a. Basic problem A general 6-D formalism is presented for the calculation of the bunch parameters (e.g. 6-D stationary beam-envelope matrix) for electron storage rings including radiation damping and quantum excitation. The problem is formulated in terms of a stochastic differential equation (SDE) and basic to our approach is th...

Cascade Stochastic Differential Equation (SDE), a continuous time model for energy dissipation in turbulence, is a generalization of the Yaglom discrete cascade model. We extend this SDE to a model in random environment by assuming that its two parameters are switched by a continuous time Markov chain whose states represent the states of the environment. Moreover, a Dirichlet process is placed ...

A numerical method for the fully adaptive sampling and interpolation of linear PDEs with random data is presented. It is based on the idea that the solution of the PDE with stochastic data can be represented as conditional expectation of a functional of a corresponding stochastic differential equation (SDE). The spatial domain is decomposed by a non-uniform grid and a classical Euler scheme is ...

In this study, COVID-19 data in Turkey is investigated by Stochastic Differential Equation Modeling (SDEM). Firstly, parameters of SDE which occur mentioned epidemic problem are estimated using the maximum likelihood procedure. Then, we have obtained reasonable (SDE) based on given data. Moreover, applying Euler-Maruyama Approximation Method trajectories achieved. The performances established C...