An interesting property of an M/M/ 1 queue, which greatly simplifies combining these queues into a network, is the surprising fact that the output of an M/M/ queue with arrival rate is a Poisson process of rate This is part of Burke's theorem, which follows from reversibility A Markov chain has the property that P[future present, past] P[future present] Conditional on the present state, future states and past states are independent
The causes of acceleration of a system--The first law of motion states that zero total force exists when the system has a constant velocity; a nonzero total force on the system causes its acceleration
Term Structure models Blacks model is concerned with describing the probability distribution of a single variable at a single point in time a term structure model describes the evolution of the whole yield curve
Derivatives Dependent on a single Underlying Variable Consider a variable, 0, (not necessarily the price of a traded security) that follows the process d e S Imagine two derivative s dependent on e with prices f, and f2. Suppose
Binomial trees are frequently used to approximate the movements in the price of a stock or other asset In each small interval of time the stock price is assumed to move up by a proportional amount u or to move down by a proportional amount d Options
