Lecture 8: Stochastic Process
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Questions and Answers

What is a characteristic of the Wiener process?

  • Being a discrete-time process
  • Having independently distributed increments (correct)
  • Having a fixed state variable
  • Always being used in finance

    • What is a common application of stochastic processes?

  • Analyzing electric and magnetic field fluctuations (correct)
  • Studying population growth
  • Developing computer algorithms
  • Predicting certain outcomes

    • What is a characteristic of random walks?

  • Being discrete-time processes (correct)
  • Having independently distributed increments
  • Always being used in finance
  • Having fixed state transitions

    • What is the purpose of considering stochastic processes in decision-making?

    <p>To take into account all expected outcomes</p> Signup and view all the answers

    What is a special case of continuous-time Markov process?

    <p>Birth-death process</p> Signup and view all the answers

    What is an application of birth-death processes?

    <p>Studying the number of customers in line</p> Signup and view all the answers

    What is a characteristic of the Wiener process in finance?

    <p>It is a continuous-time process</p> Signup and view all the answers

    What is a common area of application of stochastic processes?

    <p>All of the above</p> Signup and view all the answers

    What is a stochastic process also known as?

    <p>Random process</p> Signup and view all the answers

    What is the system that has observations at certain times in a stochastic process?

    <p>System with random variables</p> Signup and view all the answers

    What is the state space in a stochastic process?

    <p>A mathematical space where random variables are taken from</p> Signup and view all the answers

    How can a stochastic process be classified?

    <p>By its state space, index set, or dependence among random variables</p> Signup and view all the answers

    What is a stochastic process said to be if its index set contains a finite or countable number of elements?

    <p>In discrete time</p> Signup and view all the answers

    What is a characteristic of a Bernoulli process?

    <p>A sequence of independent and identically distributed random variables</p> Signup and view all the answers

    What is the Poisson process?

    <p>A stochastic process that represents a random number of points or events up to a certain time</p> Signup and view all the answers

    What is a characteristic of each random variable in a stochastic process?

    <p>Each random variable is taken from the same mathematical space</p> Signup and view all the answers

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