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A stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities. [1] Realizations of these random variables are generated and inserted into a model of the system. Outputs of the model are recorded, and then the process is repeated with a new set of random values.
In contrast, the Gillespie algorithm allows a discrete and stochastic simulation of a system with few reactants because every reaction is explicitly simulated. A trajectory corresponding to a single Gillespie simulation represents an exact sample from the probability mass function that is the solution of the master equation .
In probability theory, tau-leaping, or τ-leaping, is an approximate method for the simulation of a stochastic system. [1] It is based on the Gillespie algorithm, performing all reactions for an interval of length tau before updating the propensity functions. [2]
They provide the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability distributions, and have found application in areas including Bayesian statistics, biology, chemistry, economics, finance, information theory, physics, signal processing, and speech ...
Another significant application of stochastic processes in finance is in stochastic volatility models, which aim to capture the time-varying nature of market volatility. The Heston model [ 321 ] is a popular example, allowing for the volatility of asset prices to follow its own stochastic process.
The Dobramysl and Holcman mixed analytical-stochastic simulation model was published in 2018 by Ulrich Dobramysl and David Holcman, from the University of Cambridge and University of Oxford respectively. [3] [4] It simulates parts of Brownian trajectories, instead of simulating the entire trajectory.
Stochastic models help to assess the interactions between variables, and are useful tools to numerically evaluate quantities, as they are usually implemented using Monte Carlo simulation techniques (see Monte Carlo method). While there is an advantage here, in estimating quantities that would otherwise be difficult to obtain using analytical ...
Stochastic dynamic programming is frequently used to model animal behaviour in such fields as behavioural ecology. [ 8 ] [ 9 ] Empirical tests of models of optimal foraging , life-history transitions such as fledging in birds and egg laying in parasitoid wasps have shown the value of this modelling technique in explaining the evolution of ...