72 research outputs found
Almost sure exponential stability of numerical solutions for stochastic delay differential equations
Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (SDDEs). The important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of SDDEs directly. This is significantly different from most traditional methods by which the almost sure exponential stability is derived from the moment stability by the Chebyshev inequality and the BorelâCantelli lemma
On the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Space
Acknowledgments:
The author wishes to thank Professor Anna Chojnowska-Michalik and the
referee for many helpful suggestions and comments.We study a class of stochastic evolution equations in a Banach
space E driven by cylindrical Wiener process. Three different analytical
concepts of solutions: generalised strong, weak and mild are defined and
the conditions under which they are equivalent are given. We apply this
result to prove existence, uniqueness and continuity of weak solutions to
stochastic delay evolution equations. We also consider two examples of
these equations in non-reflexive Banach spaces: a stochastic transport
equation with delay and a stochastic delay McKendrick equation
An integral method for solving nonlinear eigenvalue problems
We propose a numerical method for computing all eigenvalues (and the
corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that
lie within a given contour in the complex plane. The method uses complex
integrals of the resolvent operator, applied to at least column vectors,
where is the number of eigenvalues inside the contour. The theorem of
Keldysh is employed to show that the original nonlinear eigenvalue problem
reduces to a linear eigenvalue problem of dimension .
No initial approximations of eigenvalues and eigenvectors are needed. The
method is particularly suitable for moderately large eigenvalue problems where
is much smaller than the matrix dimension. We also give an extension of the
method to the case where is larger than the matrix dimension. The
quadrature errors caused by the trapezoid sum are discussed for the case of
analytic closed contours. Using well known techniques it is shown that the
error decays exponentially with an exponent given by the product of the number
of quadrature points and the minimal distance of the eigenvalues to the
contour
Path Integral Monte Carlo Approach to the U(1) Lattice Gauge Theory in (2+1) Dimensions
Path Integral Monte Carlo simulations have been performed for U(1) lattice
gauge theory in (2+1) dimensions on anisotropic lattices. We extractthe static
quark potential, the string tension and the low-lying "glueball" spectrum.The
Euclidean string tension and mass gap decrease exponentially at weakcoupling in
excellent agreement with the predictions of Polyakov and G{\" o}pfert and Mack,
but their magnitudes are five times bigger than predicted. Extrapolations are
made to the extreme anisotropic or Hamiltonian limit, and comparisons are made
with previous estimates obtained in the Hamiltonian formulation.Comment: 12 pages, 16 figure
Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures
Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo
Convergence and stability analysis for modified runge-kutta methods in the numerical treatment of second kind volterra integral equations : (preprint)
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