Related papers: Quantifying model uncertainty in non-Gaussian dyna…
For non-Gaussian stochastic dynamical systems, mean exit time and escape probability are important deterministic quantities, which can be obtained from integro-differential (nonlocal) equations. We develop an efficient and convergent…
Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an $\alpha$-stable L\'evy process is still lacking.…
The mean first exit time and escape probability are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian alpha-stable type Levy motions. Both deterministic quantities are characterized by…
Motivated by the existing difficulties in establishing mathematical models and in observing the system state time series for some complex systems, especially for those driven by non-Gaussian Levy motion, we devise a method for extracting…
We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered L\'evy fluctuations, which are solutions of nonlocal elliptic equations. Firstly, we construct a new numerical scheme…
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
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…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric $\alpha$-stable L\'evy motions. Since escape probabilities are solutions of a type of integro-differential equations (i.e.,…
The emergence of the exit events from a bounded domain containing a stable fixed point induced by non-Gaussian L\'evy fluctuations plays a pivotal role in practical physical systems. In the limit of weak noise, we develop a Hamiltonian…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
The {\alpha}-stable L\'evy process, commonly used to describe L\'evy flight, is characterized by discontinuous jumps and is widely used to model anomalous transport phenomena. In this study, we investigate the associated exit problem and…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…
It is a challenging issue to analyze complex dynamics from observed and simulated data. An advantage of extracting dynamic behaviors from data is that this approach enables the investigation of nonlinear phenomena whose mathematical models…
Effects of non-Gaussian $\alpha-$stable L\'evy noise on the Gompertz tumor growth model are quantified by considering the mean exit time and escape probability of the cancer cell density from inside a safe or benign domain. The mean exit…
We present a method to learn mean residence time and escape probability from data modeled by stochastic differential equations. This method is a combination of machine learning from data (to extract stochastic differential equations as…
A dynamical system driven by non-Gaussian L\'evy noises of small intensity is considered. The first exit time of solution orbits from a bounded neighborhood of an attracting equilibrium state is estimated. For a class of non-Gaussian L\'evy…