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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...
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...
Strictly stationary solutions of multivariate ARMA equations with i.i.d. noise
Strictly stationary solutions multivariate ARMA equations i.i.d. noise
2011/6/17
We obtain necessary and sufficient conditions for the existence of strictly stationary
solutions of multivariate ARMA equations with independent and identically
distributed noise. For general ARMA(p...
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...
Probability & incompressible Navier-Stokes equations: An overview of some recent developments
incompressible Navier-Stokes Fourier transform mild solution multi-type branching random walk multiplicative cascade
2009/5/18
This is largely an attempt to provide probabilists some orientation to an important class of non-linear partial differential equations in applied mathematics, the incompressible Navier-Stokes equation...