Related papers: Minimum survival probabilities in a two-dimensiona…
We prove that multidimensional diffusions in random environment have a limiting velocity which takes at most two different values. Further, in the two-dimensional case we show that for any direction, the probability to escape to infinity in…
We investigate the first passage time t_{j,N} to a given chemical or Euclidean distance of the first j of a set of N>>1 independent random walkers all initially placed on a site of a disordered medium. To solve this order-statistics problem…
This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any…
The asymptotic survival probability of a spherical target in the presence of a single subdiffusive trap or surrounded by a sea of subdiffusive traps in a continuous Euclidean medium is calculated. In one and two dimensions the survival…
The finite element solution of two-dimensional anisotropic diffusion problems is considered. A Delaunay-type mesh condition is developed for linear finite element approximations to satisfy a discrete maximum principle. The condition is…
Continuous time random walks are non-Markovian stochastic processes, which are only partly characterized by single-time probability distributions. We derive a closed evolution equation for joint two-point probability density functions of a…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obtain the exact asymptotic behavior of the survival…
We determine the survival probability and first-passage time (FPT) to capture for a harmonically trapped particle, diffusing outside an absorbing spherical boundary by directly solving the differential equation for the survival probability.…
A number of results for reactions involving subdiffusive species all with the same anomalous exponent gamma have recently appeared in the literature and can often be understood in terms of a subordination principle whereby time t in…
We study the survival probability of an immobile target in presence of N independent diffusing walkers. We address the problem of the Mean Target Lifetime and its dependence on the number and initial distribution of the walkers when the…
We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain…
We investigate the reversible diffusion-influenced reaction of an isolated pair in the presence of a non-Markovian generalization of the backreaction boundary condition in two space dimensions. Following earlier work by Agmon and Weiss, we…
The discrete time risk model with two seasons and dependent claims is considered. An algorithm is created for computing the values of the ultimate ruin probability. Theoretical results are illustrated with numerical examples.
We consider the problem of minimizing the probability of ruin by purchasing reinsurance whose premium is computed according to the mean-variance premium principle, a combination of the expected-value and variance premium principles. We…
While there are many well-known and extensively tested results involving diffusion-limited binary reactions, reactions involving subdiffusive reactant species are far less understood. Subdiffusive motion is characterized by a mean square…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder…
Subdiffusion equation and molecule survival equation, both with Caputo fractional time derivatives with respect to another functions $g_1$ and $g_2$, respectively, are used to describe diffusion of a molecule that can disappear at any time…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…