Titlebook: Jump SDEs and the Study of Their Densities; A Self-Study Book Arturo Kohatsu-Higa,Atsushi Takeuchi Textbook 2019 Springer Nature Singapore

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Arturo Kohatsu-Higa,Atsushi Takeuchitice.Authors are among the leading academic and industrial r.In the 1970s researchers noticed that radioactive particles produced by elements naturally present in packaging material could cause bits to flip in sensitive areas of electronic chips. Research into the effect of cosmic rays on semiconduc

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Review of Some Basic Concepts of Probability Theory,In this chapter many mathematical details or proofs are not given so we refer the reader to the appropriate references in basic probability theory. See for example [10, 60].

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Simple Poisson Process and Its Corresponding SDEsPoisson processes are generalizations of the Poisson distribution which are often used to describe the random behavior of some counting random quantities such as the number of arrivals to a queue, the number of hits to a webpage etc.

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Compound Poisson Process and Its Associated Stochastic CalculusIn this chapter, we enlarge on the previous chapter by considering processes whose jumps may be random but independent between them. We also give some further definitions on general theory of stochastic processes and stochastic analysis which may be easier to understand given that they are used in this particular application.

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Basic Ideas for Integration by Parts FormulasAs explained in Sect.?8.2, the goal of this second part is to show how to obtain integration by parts (IBP) formulas for random variables which are obtained through systems based on an infinite sequence of independent random variables.