## Profile

Join date: May 13, 2022 He holds an undergraduate degree in Economics, a master's degree in Physics and a PhD in Engineering (with three years of post-doctoral work in the Institute of Robotics at the Politecnico di Torino).  In 2006 he was elected to the Italian Academy of Science. In the early 1960s, Isidori worked at the Scuola Normale Superiore, directed by Lorenzo Marsili. He became interested in the mathematical foundations of stochastic process and particularly in the classic renewal equation due to Bram Stochastic calculus. He then worked at the Politecnico di Torino, and in the middle of the 1970s he moved to the  University of Rome , where he obtained the chair of the Automatic Control Institute. Alberto Isidori is a main figure in the field of stochastic processes, which is one of the most widely studied branches of mathematics.  Under his influence, the stochastic calculus theory, developed by Bram Stochastic calculus, became one of the main pillars of stochastic processes. Stochastic processes Stochastic processes are mathematical models that describe the time-dependent evolution of a set of numbers or quantities in a random manner. The time-dependent evolution of the numbers or quantities is called the trajectory of the process.  These numbers or quantities are called random variables and they correspond to measurable functions of the time.  The random variables can be of different kinds. The following kinds of stochastic processes are known: Random walks are a stochastic process with a continuous-time evolution.  A particular instance of a random walk is the famous random walk with a constant step size. Markov processes are stochastic processes with a discrete-time evolution.  Markov processes are the basis of the Markov chains, which are the main class of stochastic processes with discrete-time evolution.  They are time-homogeneous.  They are also reversible, so the evolution from time t to t+1 is exactly the same as the evolution from t to t−1.  In particular, the process defined by the stochastic differential equation follows a Markov process. Poisson processes are stochastic processes with a continuous-time evolution. A particular instance of a Poisson process is the Poisson process with constant intensity.  It is not Markov, so it is not reversible. Continuous time Markov chains (CTMCs) are

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