Asymptotic solutions of diffusion models for risk reserves.
Asymptotic stability condition for stochastic Markovian systems of differential equations
Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by , where is a finite-valued Markov process and w(t) is a standard Wiener process, is considered. It is proved that the existence of a unique positive solution of the system of coupled Lyapunov matrix equations derived in the paper is a necessary asymptotic stability condition.
Asymptotic stability of a linear Boltzmann-type equation
We present a new necessary and sufficient condition for the asymptotic stability of Markov operators acting on the space of signed measures. The proof is based on some special properties of the total variation norm. Our method allows us to consider the Tjon-Wu equation in a linear form. More precisely a new proof of the asymptotic stability of a stationary solution of the Tjon-Wu equation is given.
Asymptotics for the -deviation of the variance estimator under diffusion
We consider a diffusion process smoothed with (small) sampling parameter . As in Berzin, León and Ortega (2001), we consider a kernel estimate with window of a function of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the deviations such as
Asymptotics for the Lp-deviation of the variance estimator under diffusion
We consider a diffusion process Xt smoothed with (small) sampling parameter ε. As in Berzin, León and Ortega (2001), we consider a kernel estimate with window h(ε) of a function α of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the Lp deviations such as
Asymptotics of a Time-Splitting Scheme for the Random Schrödinger Equation with Long-Range Correlations
This work is concerned with the asymptotic analysis of a time-splitting scheme for the Schrödinger equation with a random potential having weak amplitude, fast oscillations in time and space, and long-range correlations. Such a problem arises for instance in the simulation of waves propagating in random media in the paraxial approximation. The high-frequency limit of the Schrödinger equation leads to different regimes depending on the distance of propagation, the oscillation pattern of the initial...
Attractors for stochastic reaction-diffusion equation with additive homogeneous noise
We study the asymptotic behaviour of solutions of a reaction-diffusion equation in the whole space driven by a spatially homogeneous Wiener process with finite spectral measure. The existence of a random attractor is established for initial data in suitable weighted -space in any dimension, which complements the result from P. W. Bates, K. Lu, and B. Wang (2013). Asymptotic compactness is obtained using elements of the method of short trajectories.
Averaging and stability of quasilinear functional differential equations with Markov parameters.
Axial shear modulus of a fiber-reinforced composite with random fiber cross-sections.
Axioms for quantum probability
Backward doubly stochastic differential equations with infinite time horizon
We give a sufficient condition on the coefficients of a class of infinite horizon backward doubly stochastic differential equations (BDSDES), under which the infinite horizon BDSDES have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations.
Backward stochastic differential equations in a Lie group
Backward stochastic differential equations with oblique reflection and local Lipschitz drift.
Backward stochastic differential equations with stochastic monotone coefficients.
Backward stochastic differential equations with two distinct reflecting barriers and quadratic growth generator.
Behavior of the Euler scheme with decreasing step in a degenerate situation
The aim of this short note is to study the behavior of the weighted empirical measures of the decreasing step Euler scheme of a one-dimensional diffusion process having multiple invariant measures. This situation can occur when the drift and the diffusion coefficient are vanish simultaneously.
Besov regularity for the generalized local time of the indefinite Skorohod integral
Bilinear random integrals [Book]
Blokové logické schéma automatického optimalizátoru
Blowup and life span bounds for a reaction-diffusion equation with a time-dependent generator.