This book presents a concise and rigorous treatment of stochastic calculus. It also gives its
main applications in finance, biology and engineering. In finance, the stochastic calculus is …

A stochastic analogue of the Lotka-Volterra model for predator-prey relationship is obtained
when the birth rate of the prey and the death rate of the predator are perturbed by …

We consider a stochastic model for the development in time of a population {Zn} where the
law of offspring distribution depends on the population size. We are mainly concerned with …

Let ${\frak z}$ be a stochastic exponential, ie, ${\frak z}_t=1+\int_0^t{\frak z}_{s-}\,dM_s,$ of a
local martingale $M$ with jumps $\triangle M_t>-1$. Then ${\frak z}$ is a nonnegative local …

Supercritical branching processes are considered which are Markovian in the age structure
but where reproduction parameters may depend upon population size and even the age …

The constant volatility plain vanilla Black-Scholes model is clearly inadequate to reproduce
even plain vanilla option prices observed in the market. Efforts to build a pricing model with …

Markowitz optimal portfolio theory (Markowitz 1987), also known as the Mean-Variance
theory, has had a tremendous impact and hundreds of papers are devoted to this topic. This …

Even though the efficiency of the Polymerase chain reaction (PCR) reaction decreases,
analyses are made in terms of Galton–Watson processes, or simple deterministic models with …

We consider a branching-process model {Zn}, where the law of offspring distribution depends
on the population size. We consider the case when the means mn (mn is the mean of …

Dependence of individual reproduction upon the size of the whole population is studied in a
general branching process context. The particular feature under scrutiny is that of …