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The diffusion model has been a crucial component in studies about social networks. Many studies, especially these about influence maximization concern the proof of the submodularity of particular diffusion models. Such proofs have been…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
The article considers parameter estimation constructing such as quasi-maximum likelyhood estimation and one step estimation in statistical models generated by solution of stochastic differential equation. It has been developed a software…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…
This paper presents a tractable sufficient condition for the consistency of maximum likelihood estimators (MLEs) in partially observed diffusion models, stated in terms of stationary distribution of the associated fully observed diffusion,…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The…
Recent experiments on mucociliary clearance, an important defense against airborne pathogens, have raised questions about the topology of two-dimensional (2D) flows. We introduce a framework for studying ensembles of 2D time-invariant flow…
In this paper, we consider an optimal reinsurance problem to minimize the probability of drawdown for the scaled Cram\'er-Lundberg risk model when the reinsurance premium is computed according to the mean-variance premium principle. We…
The weak noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity frequently hidden in deterministic systems to give rise of completely new phenomena…
We study the asymptotic behaviour of the survival probability of a multitype branching process in random environment. The class of processes we consider here corresponds, in the one-dimensional situation, to the strongly subcritical case.…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
We study a one dimensional generalization of the exponential trap model using both numerical simulations and analytical approximations. We obtain the asymptotic shape of the average diffusion front in the sub-diffusive phase. Our central…
Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival…
Understanding the transport properties of a porous medium from a knowledge of its microstructure is a problem of great interest in the physical, chemical and biological sciences. Using a first-passage time method, we compute the mean…
Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…
With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and…
How many times a diffusing molecule can permeate across a membrane or be adsorbed on a substrate? We employ the encounter-based approach to find the statistics of adsorption or permeation events for molecular diffusion in a general…