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Penalized importance sampling for parameter estimation in stochastic differential equations
Chronic wasting disease Euler-Maruyama scheme Maximum likelihood estimation Partially observed discrete sparse data Penalized importance sampling Stochastic di
2013/6/14
We consider the problem of estimating parameters of stochastic differential equations with discrete-time observations that are either completely or partially observed. The transition density between t...
Estimation in Systems of Ordinary Differential Equations Linear in the Parameters
local polynomials Lotka-Volterra nonparamet-ric regression ordinary differential equation plug-in estimators
2013/6/14
Many phenomena in biology, chemistry, physics, and engineering are modeled by a system of possibly nonlinear ordinary differential equations that are linear in their unknown constants. Current methods...
On Approximation of the Backward Stochastic Differential Equation
Backward SDE approximation of the solution small noise asymptotics
2013/6/14
We consider the problem of approximation of the solution of the backward stochastic differential equation in the Markovian case. We suppose that the trend coefficient of the diffusion process depends ...
Statistical inference for discrete-time samples from affine stochastic delay differential equations
asymptotic normality composite likelihood consistency discrete time observation of continuous-time models prediction-based estimating functions pseudo-likelihood stochastic delay differential equation
2013/4/28
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to cal...
A Novel Exact Representation of Stationary Colored Gaussian Processes (Fractional Differential Approach)
Digital Filtering Filtered White Noises Power Spectral Density Fractional Brownian Motion Fractional Stochastic Differential Equation Fractional Spectral Moments
2013/4/28
A novel representation of functions, called generalized Taylor form, is applied to the filtering of white noise processes. It is shown that every Gaussian colored noise can be expressed as the output ...
Bayesian Adaptive Smoothing Spline using Stochastic Differential Equations
Adaptive smoothing Markov chain Monte Carlo Smoothing spline Stochastic dierential equation
2012/11/22
The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. How...
On characteristics of an ordinary differential equation and a related inverse problem in epidemiology
Chronic disease Compartment model Incidence Mortality Prevalence Population
2012/9/18
In this work we examine the properties of a recently described ordinary differential equation that relates the age-specific prevalence of achronic dis-ease with the incidence and mortalities of the di...
A New Class of Backward Stochastic Partial Differential Equations with Jumps and Applications
Backward Stochastic Partial Differential Equations with Jumps High-Order Partial Differential Operator Vector Partial Differential Equation Existence and Uniqueness Random Environment
2011/6/21
We formulate a new class of stochastic partial differential equations (SPDEs), named
high-order vector backward SPDEs (B-SPDEs) with jumps, which allow the high-order
integral-partial differential o...
Differential cumulants, hierachical models and monomial ideals
Differential cumulants conditional independence hierarchical mod-els monomial ideals
2011/3/21
For a joint probability density function f(x) of a random vector X the mixed partial derivatives of log f(x) can be interpreted as limiting cumulants in an infinitesimally small open neighborhood arou...
Fractional Lévy-driven Ornstein--Uhlenbeck processes and stochastic differential equations
fractional integral equation fractional Levy process fractional Levy–Ornstein–Uhlenbeck process long-range dependence p-variation Riemann–Stieltjes integration stationary solution to a fractional SDE stochastic diff erential equation
2011/3/18
Using Riemann-Stieltjes methods for integrators of bounded $p$-variation we define a pathwise integral driven by a fractional L\'{e}vy process (FLP). To explicitly solve general fractional stochastic ...
Optimal sequential change-detection for fractional stochastic differential equations
优化序贯Optimal sequential change-detection fractional stochastic differential equations
2011/3/18
The sequential detection of an abrupt and persistent change in the dynamics of an arbitrary continuous-path stochastic process is considered; the optimality of the cumulative sums (CUSUM) test is esta...
Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model
parameter identifiability differential algebra hybrid optimization
2010/10/19
Modeling viral dynamics in HIV/AIDS studies has resulted in a deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral ...
Asymptotic admissibility of priors and elliptic differential equations
Asymptotic admissibility priors elliptic differential equations
2010/3/11
We evaluate priors by the second order asymptotic behaviour of the
corresponding estimators. Under certain regularity conditions, the risk di erences
between ecient estimators of parameters taking ...
Asymptotic efficiency and finite-sample properties of the generalized profiling estimation of parameters in ordinary differential equations
Ordinary differential equations parameters estimation profiling procedure consistency asymptotic normality
2010/3/18
Ordinary differential equations (ODEs) are commonly used to
model dynamic behavior of a system. Because many parameters are
unknown and have to be estimated from the observed data, there
is growing...
Differential metrics in probability spaces。