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Consider the problem of learning the drift coefficient of a stochastic differential equation from a sample path. In this paper, we assume that the drift is parametrized by a highdimensional vector. We...
This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization takes the form of an a...
We present an ordinary differential equations approach to the analysis of algorithms for constructing l1 minimizing solutions to underdeter mined linear systems of full rank. It involves a relaxed min...
The search for a polynomial Lyapunov function proving delay-independent stability of multivariate nonlinear polynomial delay differential equations is approached using semidefinite programming. The fu...
A Study of Sto chastic Differential Equations     Differential Equations  Sto chastic       font style='font-size:12px;'> 2015/4/3
If there is a global solution Ft(x , ω), SDE is complete, also called non-explosive, conservative.
We establish that the Laplas operator with perturbation by symmetrised linear hall of displacement argument operators is the generator of unitary group in the Hilbert space of square integrable functi...
In this paper, some modifications of Adomian decomposition method are presented for solving initial value problems in ordinary differential equations. Also, the restarted and two-step methods are appl...
We carry out spectral analysis of one class of integral op- erators associated with fractional order differential equations that arise in mechanics. We establish a connection between the eigenvalues...
We use collocation methods to solve fractional boundary value problems. Analytically, we study the existence and uniquenes theorem of the collocation solutions, and discuss some error estimates. We ...
We solve four kinds of two-point boundary value problems of fractional differential equations with Caputoderivatives or Riemann-Liouville Derivatives. Analytically, we introduce the fractional Gree...
In this paper, we propose a dynamic B-spline technique using general form fourth order geometric PDEs. Basing on discretizaions of Laplace-Beltrami operator and Gaussian curvature over triangular an...
Variational formulations of three fourth order geometric partial dirential equations are derived, and based on which mixed ite element methods are presented for constructing G1 smooth B-spline sur...
We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the...
In this article, we address the dynamics and bifurcations of a wide class of stochastic differential equations around singular points where both the drift and diffusion functions vanish. We apply thes...
The matrix differential equation $x'(t) = Q(t)x(t), x(0) = x_0$ is considered in the case where $Q(t)$ is an unspecified matrix function of time, with the only constraint that $Q(t)\in \mset$ for ever...

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