{"product_id":"an-introduction-to-probability-and-stochastic-processes-9781461276432","title":"An Introduction to Probability and Stochastic Processes","description":"These notes were written as a result of my having taught a \"nonmeasure theoretic\" course in probability and stochastic processes a few times at the Weizmann Institute in Israel. I have tried to follow two principles. The first is to prove things \"probabilistically\" whenever possible without recourse to other branches of mathematics and in a notation that is as \"probabilistic\" as possible. Thus, for example, the asymptotics of pn for large n, where P is a stochastic matrix, is developed in Section V by using passage probabilities and hitting times rather than, say, pulling in Perron- Frobenius theory or spectral analysis. Similarly in Section II the joint normal distribution is studied through conditional expectation rather than quadratic forms. The second principle I have tried to follow is to only prove results in their simple forms and to try to eliminate any minor technical com- putations from proofs, so as to expose the most important steps. Steps in proofs or derivations that involve algebra or basic calculus are not shown; only steps involving, say, the use of independence or a dominated convergence argument or an assumptjon in a theorem are displayed. For example, in proving inversion formulas for characteristic functions I omit steps involving evaluation of basic trigonometric integrals and display details only where use is made of Fubini's Theorem or the Dominated Convergence Theorem.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Marc A. Berger\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/16\/2011\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 205\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.74lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.50d\u003cbr\u003e\u003cb\u003eISBN:\u003c\/b\u003e 9781461276432","brand":"Springer","offers":[{"title":"Paperback","offer_id":45063359365235,"sku":"9.78146E+12","price":93.38,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0555\/9255\/0515\/files\/img_aa279ba9-96a5-497e-bcd2-01b5b248b26f.jpg?v=1780428666","url":"https:\/\/bookstorenmore.com\/products\/an-introduction-to-probability-and-stochastic-processes-9781461276432","provider":"Bookstore N More","version":"1.0","type":"link"}