Related papers: Construction of age-structured branching processes…
We introduce an integrable stochastic process associated with the $D_2$ quantum group, which can be decomposed into two symmetric simple exclusion processes. We establish the integrability of the model under three types of boundary…
Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
A probability model is presented for the dynamics of mutation-selection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full age-specific demographic schedules. The…
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
In order to solve complex, long-horizon tasks, intelligent robots need to carry out high-level, abstract planning and reasoning in conjunction with motion planning. However, abstract models are typically lossy and plans or policies computed…
We investigate branching processes in nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out almost surely, therefore, we condition on non-extinction or…
Structural equation modeling is widely used in IS research. However, inconsistent construct definitions impede the cumulative development of knowledge. In this work, we present an approach that aims at the integration of structural equation…
In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have…
We develop a model for credit rating migration that accounts for the impact of economic state fluctuations on default probabilities. The joint process for the economic state and the rating is modelled as a time-homogeneous Markov chain.…
The p-adic numbers have found applications in a wide range of diverse fields of research. In some applications the algebraic properties of p-adics enter as an indispensable ingredient of the theory. Another class of applications has to do…
When modeling microstructures, the computational resource requirements increase rapidly as the simulation domain becomes larger. As a result, simulating a small representative fraction under periodic boundary conditions is often a necessary…
Functional limit theorems are established for continuous-state branching processes with immigration (CBIs), where the reproduction laws have finite first moments and the immigration laws exhibit large tails. Different regimes of immigration…
We show that each member of a broad class of Markovian population models induces a unique stochastic process on the space of genealogies. We construct this genealogy process and derive exact expressions for the likelihood of an observed…
In this work we study the long-time behavior for subcritical measure-valued branching processes with immigration on the space of tempered measures. Under some reasonable assumptions on the spatial motion, the branching and immigration…
This short note provides a systematic construction of market models without unbounded profits but with arbitrage opportunities.
A hierarchical system of equations is introduced to describe dynamics of `sizes' of infinite clusters which coagulate and fragmentate with homogeneous rates of certain form. We prove that this system of equations is solved weakly by…
This paper is concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction-diffusion problem when the source term depends on the density, indicating the…
We prove quenched stochastic homogenization for divergence-form elliptic equations, under the assumption that the coefficients are stationary, ergodic, integrable, and satisfy a coarse-grained ellipticity assumption. The ellipticity…
We consider a class of branching processes called Markovian binary trees, in which the individuals lifetime and reproduction epochs are modeled using a transient Markovian arrival process (TMAP). We estimate the parameters of the TMAP based…
A stochastic genetic model for biological aging is introduced bridging the gap between the bit-string Penna model and the Pletcher-Neuhauser approach. The phenomenon of exponentially increasing mortality function at intermediate ages and…