#RANDOM PROCESSES PLUS#

Thus, genetic mutations have only a minor effect in reversing the loss of genetic variation during the time frame typical for PVA. The restoration of genetic variability is slow and believed to be between 1 and 10×10 −6 genes per generation per 100 years. Morphological defects in threatened species such as the Florida panther ( Felis concolor coryi) and lack of breeding success in the Puerto Rican parrot ( Amazona vittata) appear to be a result of inbreeding depression. Inbreeding depression results in the selective removal of inbred animals and the genes carried by such animals ( Lacy, 1993). Inbreeding expression can be expressed in particular environmental conditions such as harsh winters. Inbred animals can have reduced survival, fecundity and growth (inbreeding depression). Inbreeding is defined as mating between individuals that are related by ancestry and is more likely in populations that are, or have been, small. As frequencies of alleles change at random with each successive generation, genetic variability is reduced because rarer alleles are lost by chance through the stochastic nature of birth and death. When a population is small and isolated, genetic variation is typically lost from generation to generation. Genetic stochastic processes change the frequencies of genes within a population. Lindenmayer, in Encyclopedia of Biodiversity (Second Edition), 2013 Genetic Stochastic Processes

The higher the number, the less sensitive is the oscillator. The most frequently observed parameters are nine days and 14 days. Stochastics is considered to be more sensitive than the RSI.

In both cases, as for RSIs, the vertical axis is scaled from zero to 100% levels above 70 indicate the market is overbought, and levels below 30 indicate the market is oversold. These increasingly smoothed lines are thought to generate more reliable signals than their respective counterparts. In this case the faster line is %DS which is a moving average of %D the other line is %DS-slow, a moving average of %DS. Traders often prefer a more refined version which also uses two slower lines.

A secondary line which is a moving average of this, known as %D, also plotted. In a fast stochastics graph the more sensitive line records the latest close, expressed as a percentage of the total price range over a specified period of time. It was invented by George Lane and is based on the observation that in rising markets, prices tend to close near the upper end of their price range in downtrends prices often close near the lower end. The stochastic process expands on the concept of RSIs. Moorad Choudhry, in The Bond & Money Markets, 2001 63.9.5 Stochastics Simply compute the expected returns and the volatility of the historical data, estimate them using comparable external data, or make assumptions about these values. The interesting thing about stochastic process simulation is that historical data are not necessarily required that is, the model does not have to fit any sets of historical data. The other three stochastic processes are the mean-reversion process, jump-diffusion process, and a mixed process. Four stochastic processes are included in Risk Simulator’s Forecasting tool, including geometric Brownian motion or random walk, which is the most common and prevalently used process due to its simplicity and wide-ranging applications. Hence, by stochastic simulation, we create multiple pathways of prices, obtain a statistical sampling of these simulations, and make inferences on the potential pathways that the actual price may undertake given the nature and parameters of the stochastic process used to generate the time series. The process is fixed and predetermined, but the outcomes are not. However, the price evolution over time is enveloped in a process that generates these prices. For instance, the path of a stock price is stochastic in nature, and one cannot reliably predict the exact stock price path with any certainty. A stochastic process is by definition nondeterministic, and one can plug numbers into a stochastic process equation and obtain different results every time.

#RANDOM PROCESSES PLUS#

Morton Glantz, Johnathan Mun, in Credit Engineering for Bankers (Second Edition), 2011 TheoryĪ stochastic process is nothing but a mathematically defined equation that can create a series of outcomes over time-outcomes that are not deterministic in nature that is, an equation or process that does not follow any simple discernible rule such as price will increase X% every year, or revenues will increase by this factor of X plus Y%.

Random processes