相关论文: Maximum Likelihood Estimation of Drift and Diffusi…

An approximate maximum likelihood method of estimation of diffusion parameters $(\vartheta,\sigma)$ based on discrete observations of a diffusion $X$ along fixed time-interval $[0,T]$ and Euler approximation of integrals is analyzed. We…

We study the Bayesian problems of detecting a change in the drift rate of an observable diffusion process with linear and exponential penalty costs for a detection delay. The optimal times of alarms are found as the first times at which the…

We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with…

In studying randomized search heuristics, a frequent quantity of interest is the first time a (real-valued) stochastic process obtains (or passes) a certain value. The processes under investigation commonly show a bias towards this goal,…

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the…

We discuss maximum likelihood estimation of parameters for models governed by a stochastic differential equation driven by a mixed fractional Brownian motion with random effects.

Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by…

Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…

We consider a stochastic differential equation of the form \[dX_t=\theta a(t,X_t)\,dt+\sigma_1(t,X_t)\sigma_2(t,Y_t)\,dW_t\] with multiplicative stochastic volatility, where $Y$ is some adapted stochastic process. We prove…

We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood…

Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice to perform a linear fit…

We study a utility maximization problem in a financial market with a stochastic drift process, combining a worst-case approach with filtering techniques. Drift processes are difficult to estimate from asset prices, and at the same time…

We show how to perform full likelihood inference for max-stable multivariate distributions or processes based on a stochastic Expectation-Maximisation algorithm, which combines statistical and computational efficiency in high-dimensions.…

In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…

We consider the limit distribution of maxima of periodograms for stationary processes. Our method is based on $m$-dependent approximation for stationary processes and a moderate deviation result.

We develop a maximum penalized quasi-likelihood estimator for estimating in a nonparametric way the diffusion function of a diffusion process, as an alternative to more traditional kernel-based estimators. After developing a numerical…

Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…

We consider a controlled diffusion process $(X_t)_{t\ge 0}$ where the controller is allowed to choose the drift $\mu_t$ and the volatility $\sigma_t$ from a set $\K(x) \subset \R\times (0,\infty)$ when $X_t=x$. By choosing the largest…

The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…

We consider the problem of efficient estimation of the drift parameter of an Ornstein-Uhlenbeck type process driven by a L\'{e}vy process when high-frequency observations are given. The estimator is constructed from the time-continuous…