To analyze the stability of Itô stochastic differential equations with multiplicative noise, we introduce the stochastic logarithmic norm. The logarithmic norm was originally introduced by G. Dahlquist in 1958 as a tool to study the growth of solutions to ordinary differential equations and for estimating the error growth in discretization methods for their approximate solutions. We extend the ...

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy, and in the unpinned case also conserves the momentum. We obtain a time-inhomogeneous OrnsteinUhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit...

We expand upon previous theoretical treatments of cooperation on networks by considering the effects of conditional strategies and continuous strategy space. We model agents as utility-maximizers, with utility functions over their own and their partner’s payoffs, weighted by a parameter denoting otherregard. The other-regard parameter evolves over time through learning from nearest neighbors ba...

In this article, we propose a total generalized variation (TGV) [1] based model for removing multiplicative Gamma noise. To preserve edge more, we adopt a nonconvex regularizer to TGV regularization term. The model integrates the data-fitting energy proposed in [2] with a spatially adaptive regularization parameter (SARP) approach. The data-fidelity term enables to deal with heavy multiplicativ...

The existing literature on climate change offers little guidance on why one specification or another of a “damages function” has been selected. Ideally, one wants a functional form that captures reality adequately, yet is analytically sufficiently tractable to yield useful results. This paper gives two plausible risk aversion axioms that a reduced form utility function of temperature change and...

A generalized Euler's totient is defined as a Dirichlet convolution of a power function and a product of the Souriau-Hsu-M ¨ obius function with a completely multiplicative function. Two combinatorial aspects of the generalized Euler's totient, namely, its connections to other totients and its relations with counting formulae, are investigated.

We address the minimization of regularized convex cost functions which are customarily used for edge-preserving restoration and reconstruction of signals and images. In order to accelerate computation, the multiplicative and the additive half-quadratic reformulation of the original cost-function have been pioneered in Geman & Reynolds (1992) and Geman & Yang (1995). The alternate minimization o...

We introduce an inheritance property and related table lookup structures applicable to simplified evaluation of the modular operations “multiplicative inverse”, “discrete log”, and “exponential residue” in the particular modulus 2. Regarding applications, we describe an integer representation system of Benschop for transforming integer multiplications into additions which benefits from our tabl...

Let I be a non empty set, let F be a group-like multiplicative magma family of I, and let i be an element of I. Note that F (i) is group-like. Let I be a non empty set, let F be an associative multiplicative magma family of I, and let i be an element of I. Observe that F (i) is associative. Let I be a non empty set, let F be a commutative multiplicative magma family of I, and let i be an elemen...

Following classical work by Freidlin [Trans. Amer. Math. Soc. (1988) 305 665–657] and subsequent works by Sowers [Ann. Probab. (1992) 20 504–537] and Peszat [Probab. Theory Related Fields (1994) 98 113–136], we prove large deviation estimates for the small noise limit of systems of stochastic reaction–diffusion equations with globally Lipschitz but unbounded diffusion coefficients, however, ass...