{"product_id":"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.","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":47015328579824,"sku":"9781461276432","price":84.99,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9781461276432_p0.jpg?v=1763673164","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9781461276432","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}