Search results
Results From The WOW.Com Content Network
When interpreted as time, if the index set of a stochastic process has a finite or countable number of elements, such as a finite set of numbers, the set of integers, or the natural numbers, then the stochastic process is said to be in discrete time. [54] [55] If the index set is some interval of the real line, then time is said to be continuous.
In probability theory and statistics, a continuous-time stochastic process, or a continuous-space-time stochastic process is a stochastic process for which the index variable takes a continuous set of values, as contrasted with a discrete-time process for which the index variable takes only distinct values.
A Calvo contract is the name given in macroeconomics to the pricing model that when a firm sets a nominal price there is a constant probability that a firm might be able to reset its price which is independent of the time since the price was last reset.
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.
where y is an n × 1 vector of observable state variables, u is a k × 1 vector of control variables, A t is the time t realization of the stochastic n × n state transition matrix, B t is the time t realization of the stochastic n × k matrix of control multipliers, and Q (n × n) and R (k × k) are known symmetric positive definite cost matrices.
The simplest approach is to use vector arrays of simulated or historical realizations and metadata called Stochastic Information Packets (SIPs). A set of SIPs, which preserve statistical relationships between variables, is said to be coherent and is referred to as a Stochastic Library Unit with Relationships Preserved (SLURP). SIPs and SLURPs ...
Stochastic approximation methods are a family of iterative methods typically used for root-finding problems or for optimization problems. The recursive update rules of stochastic approximation methods can be used, among other things, for solving linear systems when the collected data is corrupted by noise, or for approximating extreme values of functions which cannot be computed directly, but ...
It can be shown [1] that (), the space of stochastic processes : [,] for which the Itô integral ∫ 0 T X t d B t {\displaystyle \int _{0}^{T}X_{t}\,\mathrm {d} B_{t}} with respect to Brownian motion B {\displaystyle B} is defined, is the set of equivalence classes of P r o g {\displaystyle \mathrm {Prog} } -measurable processes in L 2 ( [ 0 ...