# Category: Stochastic models

Black–Scholes model
The Black–Scholes /ˌblæk ˈʃoʊlz/ or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the parabolic partial d
Random neural network
The random neural network (RNN) is a mathematical representation of an interconnected network of neurons or cells which exchange spiking signals. It was invented by Erol Gelenbe and is linked to the G
Stochastic homogenization
In homogenization theory, a branch of mathematics, stochastic homogenization is a technique for understanding solutions to partial differential equations with oscillatory random coefficients.
Sethi model
The Sethi model was developed by Suresh P. Sethi and describes the process of how sales evolve over time in response to advertising. The model assumes that the rate of change in sales depend on three
Cox–Ingersoll–Ross model
In mathematical finance, the Cox–Ingersoll–Ross (CIR) model describes the evolution of interest rates. It is a type of "one factor model" (short-rate model) as it describes interest rate movements as
MPMC
Massively Parallel Monte Carlo (MPMC) is a Monte Carlo method package primarily designed to simulate liquids, molecular interfaces, and functionalized nanoscale materials. It was developed originally
Dynamic scaling
Dynamic scaling (sometimes known as Family-Vicsek scaling) is a litmus test that shows whether an evolving system exhibits self-similarity. In general a function is said to exhibit dynamic scaling if
Stochastic process
In probability theory and related fields, a stochastic (/stoʊˈkæstɪk/) or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used
Voter model
In the mathematical theory of probability, the voter model is an interacting particle system introduced by Richard A. Holley and Thomas M. Liggett in 1975. One can imagine that there is a "voter" at e
Substitution model
In biology, a substitution model, also called models of DNA sequence evolution, are Markov models that describe changes over evolutionary time. These models describe evolutionary changes in macromolec
Stochastic modelling (insurance)
"Stochastic" means being or having a random variable. A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs
WSSUS model
The WSSUS (Wide-Sense Stationary Uncorrelated Scattering) model provides a statistical description of the transmission behavior of wireless channels. "Wide-sense stationarity" means the second-order m
Weighted planar stochastic lattice
Physicists often use various lattices to apply their favorite models in them. For instance, the most favorite lattice is perhaps the square lattice. There are 14 Bravais space lattice where every cell
Kolmogorov equations
In probability theory, Kolmogorov equations, including Kolmogorov forward equations and Kolmogorov backward equations, characterize continuous-time Markov processes. In particular, they describe how t
Stochastic cellular automaton
Stochastic cellular automata or probabilistic cellular automata (PCA) or random cellular automata or locally interacting Markov chains are an important extension of cellular automaton. Cellular automa
The linear-nonlinear-Poisson (LNP) cascade model is a simplified functional model of neural spike responses. It has been successfully used to describe the response characteristics of neurons in early
Stochastic chains with memory of variable length
Stochastic chains with memory of variable length are a family of stochastic chains of finite order in a finite alphabet, such as, for every time pass, only one finite suffix of the past, called contex
Restricted Boltzmann machine
A restricted Boltzmann machine (RBM) is a generative stochastic artificial neural network that can learn a probability distribution over its set of inputs. RBMs were initially invented under the name
Gilbert–Shannon–Reeds model
In the mathematics of shuffling playing cards, the Gilbert–Shannon–Reeds model is a probability distribution on riffle shuffle permutations that has been reported to be a good match for experimentally
Markov chain central limit theorem
In the mathematical theory of random processes, the Markov chain central limit theorem has a conclusion somewhat similar in form to that of the classic central limit theorem (CLT) of probability theor
Cellular Potts model
In computational biology, a Cellular Potts model (CPM, also known as the Glazier-Graner-Hogeweg model) is a computational model of cells and tissues. It is used to simulate individual and collective c
Monte Carlo molecular modeling
Monte Carlo molecular modelling is the application of Monte Carlo methods to molecular problems. These problems can also be modelled by the molecular dynamics method. The difference is that this appro
Stochastic thermodynamics
Stochastic thermodynamics is an emergent field of research in statistical mechanics that uses stochastic variables to better understand the non-equilibrium dynamics present in many microscopic systems
Affine term structure model
An affine term structure model is a financial model that relates zero-coupon bond prices (i.e. the discount curve) to a spot rate model. It is particularly useful for deriving the yield curve – the pr
Ehrenfest model
The Ehrenfest model (or dog–flea model) of diffusion was proposed by Tatiana and Paul Ehrenfest to explain the second law of thermodynamics. The model considers N particles in two containers. Particle
Ricker model
The Ricker model, named after Bill Ricker, is a classic discrete population model which gives the expected number N t+1 (or density) of individuals in generation t + 1 as a function of the number of i
Chan–Karolyi–Longstaff–Sanders process
In mathematics, the Chan–Karolyi–Longstaff–Sanders process (abbreviated as CKLS process) is a stochastic process with applications to finance. In particular it has been used to model the term structur
Interdependent networks
The study of interdependent networks is a subfield of network science dealing with phenomena caused by the interactions between complex networks. Though there may be a wide variety of interactions bet
Beverton–Holt model
The Beverton–Holt model is a classic discrete-time population model which gives the expected number n t+1 (or density) of individuals in generation t + 1 as a function of the number of individuals in
Bond fluctuation model
The BFM (bond fluctuation model or bond fluctuation method) is a lattice model for simulating the conformation and dynamics of polymer systems. There are two versions of the BFM used: The earlier vers
BIO-LGCA
In computational and mathematical biology, a biological lattice-gas cellular automaton (BIO-LGCA) is a discrete model for moving and interacting biological agents, a type of cellular automaton. The BI