Process synonyms in english8/26/2023 ![]() If you do need a specific answer, it’s likely you posed the question already in the body of the email. Use the best grammar checker available to check for common mistakes in your text.įix mistakes for free 3. ![]() Keep in touch and let me know if anything changes. Please keep me in the loop regarding any shift in our priorities. Examples: Requesting updatesKeep me informed of any updates on the project. It lets the person know that you should be kept in the loop, without requiring an immediate reply. Keep me informed …Ī phrase like “keep me informed” is appropriate when you need to be kept updated about some situation or ongoing project, but you don’t specifically need a response if nothing has changed. Examples: Asking for feedbackI’d love to hear your feedback when you have time. It also frames this information in a positive way, showing that you value their opinion but not putting too much pressure on them for a quick response. Using an expression like “I’d love to hear your feedback” shows your addressee that you expect them to comment on what you’ve said. This state space can be, for example, the integers, the real line or n, and not the entire stochastic process. Each random variable in the collection takes values from the same mathematical space known as the state space. Historically, the index set was some subset of the real line, such as the natural numbers, giving the index set the interpretation of time. The set used to index the random variables is called the index set. Introduction Ī stochastic or random process can be defined as a collection of random variables that is indexed by some mathematical set, meaning that each random variable of the stochastic process is uniquely associated with an element in the set. The theory of stochastic processes is considered to be an important contribution to mathematics and it continues to be an active topic of research for both theoretical reasons and applications. The study of stochastic processes uses mathematical knowledge and techniques from probability, calculus, linear algebra, set theory, and topology as well as branches of mathematical analysis such as real analysis, measure theory, Fourier analysis, and functional analysis. īased on their mathematical properties, stochastic processes can be grouped into various categories, which include random walks, martingales, Markov processes, Lévy processes, Gaussian processes, random fields, renewal processes, and branching processes. The values of a stochastic process are not always numbers and can be vectors or other mathematical objects. If the random variables are indexed by the Cartesian plane or some higher-dimensional Euclidean space, then the collection of random variables is usually called a random field instead. But often these two terms are used when the random variables are indexed by the integers or an interval of the real line. The terms stochastic process and random process are used interchangeably, often with no specific mathematical space for the set that indexes the random variables. The term random function is also used to refer to a stochastic or random process, because a stochastic process can also be interpreted as a random element in a function space. These two stochastic processes are considered the most important and central in the theory of stochastic processes, and were discovered repeatedly and independently, both before and after Bachelier and Erlang, in different settings and countries. Erlang to study the number of phone calls occurring in a certain period of time. Examples of such stochastic processes include the Wiener process or Brownian motion process, used by Louis Bachelier to study price changes on the Paris Bourse, and the Poisson process, used by A. ![]() Īpplications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, cryptography, and telecommunications. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. In probability theory and related fields, a stochastic ( / s t ə ˈ k æ s t ɪ k/) or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence has the interpretation of time. ![]() The Wiener process is widely considered the most studied and central stochastic process in probability theory. A computer-simulated realization of a Wiener or Brownian motion process on the surface of a sphere.
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