Related papers: On the exit time from open sets of some semi-Marko…
We report a direct experimental observation and provide a theory of the distribution of trajectories along which a fluctuating system moves over a potential barrier in escape from a metastable state. The experimental results are obtained…
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…
In this paper we identify the asymptotic tail of the distribution of the exit time $\tau_C$ from a cone $C$ of an isotropic $\alpha$-self-similar Markov process $X_t$ with a skew-product structure, that is $X_t$ is a product of its radial…
While criticality is widely observed in neural networks, its underlying neural mechanism is not known well. We consider a network of $N$ excitatory leaky integrated and fire (LIF) neurons that reside on a regular lattice with periodic…
We develop a framework for non-Markovian, well-mixed SIR and SIS models beyond mean field, utilizing the continuous-time random walk formalism. Using a gamma distribution for the infection and recovery inter-event times as a test case, we…
We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene…
We study stochastic tree fluid networks driven by a multidimensional Levy process. We are interested in (the joint distribution of) the steady-state content in each of the buffers, the busy periods, and the idle periods. To investigate…
In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature…
There is a wide range of mathematical models that describe populations of large numbers of neurons. In this article, we focus on nonlinear noisy leaky integrate-and-fire (NNLIF) models that describe neuronal activity at the level of the…
Let $X$ be a real valued L\'evy process that is in the domain of attraction of a stable law without centering with norming function $c.$ As an analogue of the random walk results in \cite{vw} and \cite{rad} we study the local behaviour of…
We discuss the first passage time problem in the semi-infinite interval, for homogeneous stochastic Markov processes with L{\'e}vy stable jump length distributions $\lambda(x)\sim\ell^{\alpha}/|x|^{1+\alpha}$ ($|x|\gg\ell$), namely,…
This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with semi-uniform Feller transition probabilities. The important…
In this article, we provide different representations for a time-fractional birth and death process $N_{\alpha}(t)$, whose transition probabilities are governed by a time-fractional system of differential equations. More specifically, we…
We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modelled as a stochastic process with a fat-tailed non-exponential distribution of waiting times, mimicking long-term…
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…
In this paper, we study the asymptotic of exit problem for controlled Markov diffusion processes with random jumps and vanishing diffusion terms, where the random jumps are introduced in order to modify the evolution of the controlled…
We introduce and investigate the escape problem for random walkers that may eventually die, decay, bleach, or lose activity during their diffusion towards an escape or reactive region on the boundary of a confining domain. In the case of a…
In this paper we study positive self-similar Markov processes obtained by (partially) resurrecting a strictly $\alpha$-stable process at its first exit time from $(0,\infty)$. We construct those processes by using the Lamperti transform. We…
In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…
We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…