Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
THE THEORY OF STOCASTIC PROCESSES MAT 605 0 3 + 0 3 6
Ön Koşul Dersleri Students are assumed to be familiar with Analysis I-II, Linear Algebra I-II, and Probability
 Dersin Dili Türkçe Dersin Seviyesi Doktora Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. HALİM ÖZDEMİR Dersi Verenler Dersin Yardımcıları Res.Asssist. Emre Kişi and Res.Assist. Tuğba Petik Dersin Kategorisi Alanına Uygun Öğretim Dersin Amacı In the modern approach to stochastic processes, the primary object is the behavior of sample paths. This is especially so for the applied scientist and engineer, since it is the sample path which he observes and tries to control. Considerations in this course construct the bridge between mathematician and applied scientist. Dersin İçeriği Probability spaces and random variables. Expectations and independence. Bernoulli processes and sums of independent random variables. Poisson processes. Markov chains. Limiting behavior. Applications of Markov chains. Markov processes.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she consolidates the concept of probability 1 - 2 - A - C - 2 - He/she consolidates the concept of random variables 1 - 2 - 14 - A - C - 3 - He/she understands the concept of expected value and independence 1 - 2 - 4 - 14 - 15 - A - C - D - 4 - He/she sees some stochastic processes 1 - 2 - 4 - 14 - 15 - A - C - D - 5 - He/she applies some stochastic processes 1 - 2 - 4 - 14 - 15 - A - C - D - 6 - He/she constructs the bridge between mathematics and daily life. 1 - 2 - 4 - 14 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 14:Self Study 4:Drilland Practice 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework D:Project / Design

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Probability spaces and random variables [1] pages 1-21
2 Expectations and independence [1] pages 21-43
3 Bernoulli processes and sums of independent random variables [1] pages 43-70
4 Bernoulli processes and sums of independent random variables (continuation) [1] pages 43-70
5 Poisson processes [1] pages 70-106
6 Poisson processes (continuation) [1] pages 70-106
7 Markov chains [1] pages 106-144
8 Markov chains (continuation) [1] pages 106-144
9 Limiting behavior [1] pages 144-169
10 Limiting behavior (continuation) [1] pages 144-169
11 Applications of Markov chains [1] pages 169-194
12 Applications of Markov chains (continuation) [1] pages 169-194
13 Markov processes [1] pages 232-282
14 Markov processes (continuation) [1] pages 232-282

#### Kaynaklar

Ders Notu [1] Çınlar, E., Introduction to stochastic processes, Prentice-Holl, Inc., New Jersey, 1975.
Ders Kaynakları [2] Brzezniak, Z. and Zastawniak, T., Basic Stochastic Processes, Springer-Verlag, New York, 1998.>

[3] Hoel, P. G., Port, S. C. and Stone, C. J., Introduction to stochastic processes, University of California, Los Angeles, 1993.

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
PerformansGoreviSeminer 1 40
Odev 1 20
AraSinav 1 40
Toplam 100
Yıliçinin Başarıya Oranı 60
Finalin Başarıya Oranı 40
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 15 15
Assignment 1 8 8
Performance Task (Seminar) 1 20 20
Final examination 1 20 20
Toplam İş Yükü 159
Toplam İş Yükü /25(s) 6.36
Dersin AKTS Kredisi 6.36
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