Approximations of the brownian rough path with applications to stochastic analysis
Approximations to mild solutions of stochastic semilinear equations.
Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients
In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.
A.s. approximation results for multiplicative stochastic integrals
Assessing effects of HIV heterogeneity and macrophage on the HIV pathogenesis in HIV-infected individuals.
Asymptotic and exponential decay in mean square for delay geometric Brownian motion
We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions of the geometric Brownian motion with delay. The conditions are written in terms of the parameters and are explicit for the case of asymptotic decay. For exponential decay, they are easily resolvable numerically. The analytical method is based on construction of a Lyapunov functional (asymptotic decay) and a forward-backward estimate for the square mean (exponential decay).
Asymptotic and transient analysis of stochastic core ecosystem models.
Asymptotic behavior of differential equations driven by periodic and random processes with slowly decaying correlations
We consider a differential equation with a random rapidly varying coefficient. The random coefficient is a gaussian process with slowly decaying correlations and compete with a periodic component. In the asymptotic framework corresponding to the separation of scales present in the problem, we prove that the solution of the differential equation converges in distribution to the solution of a stochastic differential equation driven by a classical brownian motion in some cases, by a fractional brownian...
Asymptotic behavior of differential equations driven by periodic and random processes with slowly decaying correlations
We consider a differential equation with a random rapidly varying coefficient. The random coefficient is a Gaussian process with slowly decaying correlations and compete with a periodic component. In the asymptotic framework corresponding to the separation of scales present in the problem, we prove that the solution of the differential equation converges in distribution to the solution of a stochastic differential equation driven by a classical Brownian motion in some cases, by a fractional Brownian motion...
Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion
We prove, by means of Malliavin calculus, the convergence in of some properly renormalized weighted quadratic variations of bi-fractional Brownian motion (biFBM) with parameters and , when and .
Asymptotic behaviour of stochastic quasi dissipative systems
We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.
Asymptotic behaviour of stochastic quasi dissipative systems
We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.
Asymptotic behaviour of stochastic semigroups.
The problem to be treated in this note is concerned with the asymptotic behaviour of stochastic semigroups, as the time becomes very large. The subject is largely motived by the Theory of Markov processes. Stochastic semigroups usually arise from pure probabilistic problems such as random walks stochastic differential equations and many others.An outline of the paper is as follows. Section one deals with the basic definitions relative to K-positivity and stochastic semigroups. Asymptotic behaviour...
Asymptotic evaluation of the Poisson measures for tubes around jump curves
We find the asymptotic behavior of P(||X-ϕ|| ≤ ε) when X is the solution of a linear stochastic differential equation driven by a Poisson process and ϕ the solution of a linear differential equation driven by a pure jump function.
Asymptotic expansion of stochastic oscillatory integrals with rotation invariance
Asymptotic growth of spatial derivatives of isotropic flows.
Asymptotic normality of eigenvalues of random ordinary differential operators
Boundary value problems for ordinary differential equations with random coefficients are dealt with. The coefficients are assumed to be Gaussian vectorial stationary processes multiplied by intensity functions and converging to the white noise process. A theorem on the limit distribution of the random eigenvalues is presented together with applications in mechanics and dynamics.
Asymptotic Properties of Stochastic Semilinear Equations by the Method of Lower Measures
Asymptotic solutions of diffusion models for risk reserves.