Renewal theory for extremal Markov sequences of Kendall type

analysis of ruin probability for insurance companies using markov chain

در این پایان نامه نشان داده ایم که چگونه می توان مدل ریسک بیمه ای اسپیرر اندرسون را به کمک زنجیره های مارکوف تعریف کرد. سپس به کمک روش های آنالیز ماتریسی احتمال برشکستگی ، میزان مازاد در هنگام برشکستگی و میزان کسری بودجه در زمان وقوع برشکستگی را محاسبه کرده ایم. هدف ما در این پایان نامه بسیار محاسباتی و کاربردی تر از روش های است که در گذشته برای محاسبه این احتمال ارائه شده است. در ابتدا ما نشا...

Markov Renewal Theory Applied to Performability Evaluation

Computer and communication systems are designed to meet a certain speciied behavior. The procurement of metrics to establish how well the system behaves, that is, how closely it follows the speciied behavior , is the objective of quantitative analysis. Traditionally, performance and dependability evaluation are used as separate approaches to provide quantitative gures of system behavior. Perfor...

Extremal functions for sequences

Davenport-Schinzel sequences DS(s) are finite sequences of some symbols with no immediate repetition and with no alternating subsequence (i.e. of the type ababab . . .) of the length s. This concept based on a geometrical motivation is due to Davenport and Schinzel in the middle of sixties. In the late eighties strong lower and upper (superlinear) bounds on the maximum length of the DS(s) seque...

Renewal Theorems for Markov Chains

A Linear Upper Bound in Extremal Theory of Sequences

An extremal problem considering sequences related to Davenport-Schinzel sequences is investigated in this paper. We prove that f(x1x i 2..x i kx i 1x i 2..x i k, n) = O(n) where the quantity on the left side is defined as the maximum length m of the sequence u = a1a2..am of integers such that 1) 1 ≤ ar ≤ n, 2) ar = as, r 6= s implies |r− s| ≥ k and 3) u contains no subsequence of the type x1......