for R(t) which is rapidly convergent for small values of t and which incidentally provides a new set of inequalities. The rapidity of convergence is compared with a series for R(t) and with the Laplace C.F. for R(t). This assessment is similar to recent work by Teichroew (1952) on the comparative rapidity of convergence of series ando.F.'s for the elementary function e?, hi (1 + x) and arc tan ...

Throughout this paper, we always assume thatH is a real Hilbert space, whose inner product and norm are denoted by 〈·, ·〉 and ‖ · ‖. The symbols → and ⇀ are denoted by strong convergence and weak convergence, respectively. ωw xn {x : ∃xni ⇀ x} denotes the weak w-limit set of {xn}. Let C be a nonempty closed and convex subset of H and T : C → C a mapping. In this paper, we denote the fixed point...

We propose a strategy to achieve the fastest convergence in the Wang-Landau algorithm with varying modification factors. With this strategy, the convergence of a simulation is at least as good as the conventional Monte Carlo algorithm, i.e., the statistical error vanishes as 1/sqrt t, where t is a normalized time of the simulation. However, we also prove that the error cannot vanish faster than...

Throughout this paper, we always assume thatH is a real Hilbert space, whose inner product and norm are denoted by 〈·, ·〉 and ‖ · ‖. The symbols → and ⇀ are denoted by strong convergence and weak convergence, respectively. ωw xn {x : ∃xni ⇀ x} denotes the weak w-limit set of {xn}. Let C be a nonempty closed and convex subset of H and T : C → C a mapping. In this paper, we denote the fixed point...

We prove the convergence of a first order finite difference scheme approximating a non local eikonal Hamilton-Jacobi equation. The non local character of the problem makes the scheme not monotone in general. However, by using in a convenient manner the convergence result for monotone scheme of Crandall Lions, we obtain the same bound |∆X| + ∆t for the rate of convergence.

We characterize convergence of a sequence of d-dimensional random vectors by convergence of the one-dimensional margins and of the copula. The result is applied to the approximation of portfolios modelled by t-copulas with large degrees of freedom, and to the convergence of certain dependence measures of bivariate distributions. AMS 2000 Subject Classifications: primary: 60F05, 62H05 secondary:...

We consider, for ρ ∈ [0,1] and ε > 0 small, the nonautonomous weakly damped wave equation with a singularly oscillating external force ∂2 t u− u+ γ ∂tu=−f (u)+ g0(t)+ ε−ρg1(t/ε), together with the averaged equation ∂2 t u− u+ γ ∂tu=−f (u)+ g0(t). Under suitable assumptions on the nonlinearity and the external force, we prove the uniform (with respect to ε) boundedness of the attractors Aε in th...

for short) if C lira f ( t ) := lira 1 i t t -oo t--.oo-[ Jo f ( s )ds = foo. If ,-~lim f ( t ) = foo, then C lim f ( t ) = foo; and if C lira f ( t ) = foo, then A lim f ( t ) = f ~ . The converse implicat ions are false, in general. Addi t ional condit ions which allow the inverse implicat ion are called Tauber ian conditions, and the corresponding s ta tements Tauber ian theorems. Here we ar...

and Applied Analysis 3 Now we present some lemmas to be used later for the proof of the convergence theorem. Consider a right continuous process YΔ l = {YΔ (t), t ∈ [−γ, T]}. YΔ l is called a discrete-time numerical approximationwithmaximum step size Δ l , if it is obtained by using a time discretization t Δ l , and the random variable YΔ l tn is F tn -measurable for n ∈ {1, . . . , N}. Further...

Recently, many variance reduced stochastic alternating direction method of multipliers (ADMM) methods (e.g. SAGADMM, SDCA-ADMM and SVRG-ADMM) have made exciting progress such as linear convergence rates for strongly convex problems. However, the best known convergence rate for general convex problems is O(1/T ) as opposed to O(1/T ) of accelerated batch algorithms, where T is the number of iter...