Lecture

Applied Probability & Stochastic Processes

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Description

This lecture covers the fundamental concepts of applied probability and stochastic processes, focusing on topics such as transition probability matrices, Markov chains, and characteristic polynomials. The instructor explains the n-step transition probability matrix, eigenvalues, and linear combinations of matrices. The lecture also delves into communication classes, recurrent and transient states, and the Cayley-Hamilton theorem. Various exercises explore random walks, invariant distributions, and expected return times in different scenarios.

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Related concepts (32)

Markov chain

A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC).

Communication

Communication is usually defined as the transmission of information. The term can also refer to the message itself, or the field of inquiry studying these transmissions, also known as communication studies. The precise definition of communication is disputed. Controversial issues are whether unintentional or failed transmissions are included and whether communication does not just transmit meaning but also create it. Models of communication aim to provide a simplified overview of its main components and their interaction.

Intercultural communication

Intercultural communication is a discipline that studies communication across different cultures and social groups, or how culture affects communication. It describes the wide range of communication processes and problems that naturally appear within an organization or social context made up of individuals from different religious, social, ethnic, and educational backgrounds. In this sense, it seeks to understand how people from different countries and cultures act, communicate, and perceive the world around them.

Organizational communication

Within the realm of communication studies, organizational communication is a field of study surrounding all areas of communication and information flow that contribute to the functioning of an organization . Organizational communication is constantly evolving and as a result, the scope of organizations included in this field of research have also shifted over time. Now both traditionally profitable companies, as well as NGO's and non-profit organizations, are points of interest for scholars focused on the field of organizational communication.

Nonverbal communication

Nonverbal communication (NVC) is the transmission of messages or signals through a nonverbal platform such as eye contact, facial expressions, gestures, posture, use of objects and body language. It includes the use of social cues, kinesics, distance (proxemics) and physical environments/appearance, of voice (paralanguage) and of touch (haptics). A signal has three different parts to it, including the basic signal, what the signal is trying to convey, and how it is interpreted.

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