{"product_id":"9789811002717","title":"Poisson Point Processes and Their Application to Markov Processes","description":"An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ∈ S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S \\ {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a one-to-one correspondence between a recurrent extension and a pair of a positive measure k(db) on S \\ {a} (called the jumping-in measure and a non-negative number m\u0026lt; (called the stagnancy rate). The necessary and sufficient conditions for a pair k, m was obtained so that the correspondence is precisely described. For this, Itô used,  as a fundamental tool, the notion of Poisson point processes formed of all excursions of  the process on S \\ {a}. This theory of Itô's of Poisson point processes of excursions is indeed a breakthrough. It has been expanded and applied to more general extension problems by many succeeding researchers. Thus we may say that this lecture note by Itô is really a memorial work in the extension problems of Markov processes. Especially in Chapter 1 of this note, a general theory of Poisson point processes is given that reminds us of Itô's beautiful and impressive lectures in his day.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ePublication Year: \u003c\/strong\u003e2015\u003cbr\u003e\u003cstrong\u003eImprint: \u003c\/strong\u003eSpringer Singapore\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003eFormat: P\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003eWeight (Gram): 1007\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003c\/p\u003e","brand":"Kiyosi Itô","offers":[{"title":"Default Title","offer_id":41266937266354,"sku":"9789811002717","price":1106418.39,"currency_code":"IDR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0502\/5382\/4178\/products\/9811002711.01_SCLZZZZZZZ.jpg?v=1636030524","url":"https:\/\/readabook.store\/en-id\/products\/9789811002717","provider":"READABOOK BY ALKEM","version":"1.0","type":"link"}