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Carleman Estimate for Stochastic Parabolic Equations and Inverse Stochastic Parabolic Problems
Stochastic parabolic equations Carleman estimate conditional stability inverse source problem
2011/9/22
Abstract: In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we solve two inverse problems for stochastic parabolic equations. One is co...
Homogenization of a stochastic nonlinear reaction-diffusion equation with a large reaction term: the almost periodic framework
Stochastic Homogenization Almost Periodic Stochastic Reaction-Diffusion Equations Wiener Process
2011/9/21
Abstract: Homogenization of a stochastic nonlinear reaction-diffusion equation with a large non- linear term is considered. Under a general Besicovitch almost periodicity assumption on the coefficient...
The Role of Stochastic Re-acceleration in the Prompt Emission of Gamma-Ray Bursts: Application to Hadronic Injection
Stochastic Re-acceleration Prompt Emission Gamma-Ray Bursts: Application Hadronic Injection
2011/10/20
We study effects of particle re-acceleration in the post-shock region via magnetohydrodynamic/plasma turbulence, in the context of a mixed hadronic-leptonic model for the prompt emission of gamma-ray ...
Predictable projections of conformal stochastic integrals: an application to Hermite series and to Widder's representation
conformal stochastic integrals Widder's representation Hermite series
2011/9/21
Abstract: In this article, we study predictable projections of stochastic integrals with respect to the conformal Brownian motion, extending the connection between powers of the conformal Brownian mot...
Multiplicative white noise functionals and the Krylov-Veretennikov expansion for coalescing stochastic flows
Krylov-Veretennikov expansion coalescing stochastic flows Probability
2011/9/20
Abstract: In this article we consider multiplicative operator-valued white noise functionals related to a stochastic flow. A generalization of the Krylov-Veretennikov expansion is presented. An analog...
Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models
Stochastic theory large-scale enzyme-reaction networks Finite copy number corrections
2011/8/18
Abstract: Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtolitres. Physiological concentrations realized in such small volumes imply low copy numbers of inter...
Uniform moment bounds of multi-dimensional functions of discrete-time stochastic processes
stochastic stability Markov chains uniform moment bounds invariant distributions stochastic control
2011/9/20
Abstract: We establish conditions for uniform $r$-th moment bound of certain $\R^d$-valued functions of a discrete-time stochastic process taking values in a general metric space. The conditions inclu...
Averaging approximation to singularly perturbed nonlinear stochastic wave equations
stochastic nonlinear wave equations averaging tightness martingale
2011/9/16
Abstract: An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on...
Stochastic Service Systems, Random Interval Graphs and Search Algorithms
Queueing theory interval graphs Lambert series asymptotic expansions
2011/9/15
Abstract: We consider several stochastic service systems, and study the asymptotic behavior of the moments of various quantities that have application to models for random interval graphs and algorith...
The impact of a stochastic gravitational-wave background on pulsar timing parameters
impact stochastic gravitational-wave background timing parameters
2011/10/12
Gravitational waves are predicted by Einstein's theory of general relativity as well as other theories of gravity. The rotational stability of the fastest pulsars means that timing of an array of thes...
Exact solution of a stochastic protein dynamics model with delayed degradation
protein dynamics model
2011/9/29
We study a stochastic model of protein dynamics that explicitly includes delay in the degradation.We rigorously derive the master equation for the processes and solve it exactly. We show that the equa...
A linear stochastic differential equation driven by a fractional Brownian motion with Hurst parameter >1/2
Linear stochastic differential equation Fractional Brownian motion Stochastic calculus Ito formula
2011/9/15
Abstract: Given a fractional Brownian motion \,\,$(B_{t}^{H})_{t\geq 0}$,\, with Hurst parameter \,$> 1/2$\,\,we study the properties of all solutions of \,\,: {equation} X_{t}=B_{t}^{H}+\int_0^t X_{u...
Global Uniqueness for an Inverse Stochastic Hyperbolic Equation with Three Unknowns
Global uniqueness inverse stochastic hyperbolic equation Carleman estimate three unknowns
2011/9/13
Abstract: This paper is addressed to an inverse stochastic hyperbolic equation with three unknowns, i.e., a source term, an initial displacement and an initial velocity. The global uniqueness is prove...
A trajectorial interpretation of the dissipations of entropy and Fisher information for stochastic differential equations
entropy and Fisher information stochastic differential equations Probability
2011/9/13
Abstract: We introduce and develop a pathwise description of the dissipation of general convex entropies for continuous time Markov processes, based on simple backward martingales and convergence theo...
Rare event simulation for processes generated via stochastic fixed point equations
Monte Carlo methods importance sampling perpetuities large deviations nonlinear renewal theory Harris recurrent Markov chains
2011/9/13
Abstract: In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable V satisfying the distributional...