Stochastic Methods in Biology

I. Population genetics.- [1] A stochastic model of compensatory neutral evolution.- [2] Some models for treating evolution of multigene families and other repetitive DNA sequences.- [3] A genealogical description of the infinitely-many neutral alleles model.- [4] Equilibrium measures of the stepping stone model with selection in population genetics.- [5] Asymptotic properties for Kimura's diffusion model with altruistic allele.- II. Measure-valued diffusion processes related to population genetics.- [6] The infinitely-many-alleles model with selection as a measure-valued diffusion.- [7] Multi-allelic Gillespie-Sato diffusion models and their extension to infinite allelic ones.- [8] Stationary distribution of a diffusion process taking values in probability distributions on the partitions.- III. Neurophysiology.- [9] Weak convergence of stochastic neuronal models.- [10] Note on the Ornstein-Uhlenbeck process model for stochastic activity of a single neuron.- IV. Fluctuation in living cells.- [11] Fluctuation in living cells: effect of field fluctuation and asymmetry of fluctuation.- [12] Some aspects of Oosawa's equation.- V. Mathematical methods related to other problems in biology, epidemiology, population dynamics, etc..- [13] Problems of epidemic modelling.- [14] Markov semigroups associated with one-dimensional Lévy operators --regularity and convergence--.- [15] On some conditions for diffusion processes to stay on the boundary of a domain.- [16] The point interaction approximation for diffusion in regions with many small holes.- [17] Unimodality and bounds of modes for distributions of generalized sojourn times.- [18] Fluctuation in population dynamics.