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Huijie Qiao

Publications and source records attributed to Huijie Qiao.

54 records · Page 3Linked to original sources
arXiv2020

Path independence of the additive functionals for McKean-Vlasov stochastic differential equations with jumps

In this article, the path independent property of additive functionals of McKean-Vlasov stochastic differential equations with jumps is characterised by nonlinear partial integro-differential equations involving $L$-derivatives with respect to probability measures introduced by P.-L. Lions. Our result extends the recent work [16] by Ren and Wang where their concerned McKean-Vlasov stochastic differential equations are driven by Brownian motions.

math.PR↗
arXiv2020

Support theorems for degenerate stochastic differential equations with jumps and applications

In the paper, we are concerned with degenerate stochastic differential equations with jumps. Firstly, we establish two support theorems for the solutions of the degenerate stochastic equations, under different (sufficient) conditions. Secondly, we apply one of our support theorems to a class of degenerate stochastic evolution equations (i.e., infinite-dimensional stochastic differential equations) with jumps to get a characterisation of path-independence for the densities of their Girsanov transformations.

math.PR↗
arXiv2020

Convergence of nonlinear filterings for multiscale systems with correlated Lévy noises

In the paper, we consider nonlinear filtering problems of multiscale systems in two cases-correlated sensor Lévy noises and correlated Lévy noises. First of all, we prove that the slow part of the origin system converges to the homogenized system in the uniform mean square sense. And then based on the convergence result, in the case of correlated sensor Lévy noises, the nonlinear filtering of the slow part is shown to approximate that of the homogenized system in $L^1$ sense. However, in the case of correlated Lévy noises, we prove that the nonlinear filtering of the slow part converges weakly to that of the homogenized system.

math.PR↗
arXiv2019

Convergence of Nonlinear Filtering for Stochastic Dynamical Systems with Lévy Noises

We consider a nonlinear filtering problem of multiscale non-Gaussian signal processes and observation processes with jumps. Firstly, we prove that the dimension for the signal system can be reduced by a homogenized approach. Secondly, convergence of the corresponding nonlinear filtering to the homogenized filtering is shown by a weak convergence technique. Finally, we give an example to explain our result.

math.PR↗
arXiv2019

Effective Filtering for Multiscale Stochastic Dynamical Systems in Hilbert Spaces

In the paper, effective filtering for a type of slow-fast data assimilation systems in Hilbert spaces is considered. Firstly, the system is reduced to a system on a random invariant manifold. Secondly, nonlinear filtering of the origin system can be approximated by that of the reduction system. Finally, we apply the obtained result to an example.

math.PR↗
arXiv2018

Effective filtering analysis for non-Gaussian dynamic systems

This work is about a slow-fast data assimilation system under non-Gaussian noisy fluctuations. Firstly, we show the existence of a random invariant manifold for a stochastic dynamical system with non-Gaussian noise and two-time scales. Secondly, we obtain a low dimensional reduction of this system via a random invariant manifold. Thirdly, we prove that the low dimensional filter on the random invariant manifold approximates the original filter, in a probabilistic sense.

math.PR↗
arXiv2018

A Multiplicative Ergodic Theorem for Discontinuous Random Dynamical Systems and Applications

Motivated by studying stochastic systems with non-Gaussian Lévy noise, spectral properties for a type of linear cocycles are considered. These linear cocycles have countable jump discontinuities in time. A multiplicative ergodic theorem is proved for such linear cocycles. Then, the result is illustrated for two linear stochastic systems with general Lévy motions.

math.PR↗
arXiv2018

On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces

Based on a recent result on characterising the path-independence of the Girsanov transformation for non-Lipschnitz stochastic differential equations (SDEs) with jumps on $R^d$, in this paper, we extend our consideration of characterising the path-indpendent property from finite-dimensional SDEs with jumps to stochastic evolution equations with jumps in Hilbert spaces. This is done via Galerkin type finite-dimensional approximations of the infinite-dimensional stochastic evolution equations with jumps in the manner that one could then link the characterisation of the path-independence for finite-dimensional jump type SDEs to that for the infinite-dimensional settings. Our result provides an intrinsic link of infinite-dimensional stochastic evolution equations with jumps to infinite-dimensional partial integro-differential equations.

math.PR↗
arXiv2018

Effective Filtering on a Random Slow Manifold

This work is about a slow-fast data assimilation system when only slow components are observable. First, we obtain its low dimensional reduction via an invariant slow manifold. Second, we prove that the low dimensional filter on the slow manifold approximates the original filter in a suitable metric. Finally, we illustrate this approximate filter numerically in an example.

math.PR↗
arXiv2015

A Global Map of Suitability for Coastal Vibrio cholerae Under Current and Future Climate Conditions

Vibrio cholerae is a globally distributed water-borne pathogen that causes severe diarrheal disease and mortality, with current outbreaks as part of the seventh pandemic. Further understanding of the role of environmental factors in potential pathogen distribution and corresponding V. cholerae disease transmission over time and space is urgently needed to target surveillance of cholera and other climate and water-sensitive diseases. We used an ecological niche model (ENM) to identify environmental variables associated with V. cholerae presence in marine environments, to project a global model of V. cholerae distribution in ocean waters under current and future climate scenarios. We generated an ENM using published reports of V. cholerae in seawater and freely available remotely sensed imagery. Models indicated that factors associated with V. cholerae presence included chlorophyll-a, pH, and sea surface temperature (SST), with chlorophyll-a demonstrating the greatest explanatory power from variables selected for model calibration. We identified specific geographic areas for potential V. cholerae distribution. Coastal Bangladesh, where cholera is endemic, was found to be environmentally similar to coastal areas in Latin America. In a conservative climate change scenario, we observed a predicted increase in areas with environmental conditions suitable for V. cholerae. Findings highlight the potential for vulnerability maps to inform cholera surveillance, early warning systems, and disease prevention and control.

q-bio.PE↗
arXiv2014

Asymptotic methods for stochastic dynamical systems with small non-Gaussian Lévy noise

The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric $α$-stable Lévy motions. Since escape probabilities are solutions of a type of integro-differential equations (i.e., differential equations with nonlocal interactions), asymptotic methods are offered to solve these equations to obtain escape probabilities when noises are sufficiently small. Three examples are presented to illustrate the asymptotic methods, and asymptotic escape probability is compared with numerical simulations.

math.PR↗
arXiv2014

Stationary Measures for Stochastic Differential Equations with Jumps

In the paper, stationary measures of stochastic differential equations with jumps are considered. Under some general conditions, existence of stationary measures is proved through Markov measures and Lyapunov functions. Moreover, for two special cases, stationary measures are given by solutions of Fokker-Planck equations and long time limits for the distributions of system states.

math.PR↗
arXiv2012

Topological equivalence for discontinuous random dynamical systems and applications

After defining non-Gaussian Lévy processes for two-sided time, stochastic differential equations with such Lévy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in time. Topological equivalence (or conjugacy) for such an Itô stochastic differential equation and its transformed random differential equation is established. Consequently, a stochastic Hartman-Grobman theorem is proved for the linearization of the Itô stochastic differential equation. Furthermore, for Marcus stochastic differential equations,this topological equivalence is used to prove existence of global random attractors.

math.PR↗
arXiv2012

Escape Probability for Stochastic Dynamical Systems with Jumps

The escape probability is a deterministic concept that quantifies some aspects of stochastic dynamics. This issue has been investigated previously for dynamical systems driven by Gaussian Brownian motions. The present work considers escape probabilities for dynamical systems driven by non-Gaussian Lévy motions, especially symmetric $α$-stable Lévy motions. The escape probabilities are characterized as solutions of the Balayage-Dirichlet problems of certain partial differential-integral equations. Differences between escape probabilities for dynamical systems driven by Gaussian and non-Gaussian noises are highlighted. In certain special cases, analytic results for escape probabilities are given.

math.DS↗