{"id":863,"date":"2026-01-11T09:18:43","date_gmt":"2026-01-11T17:18:43","guid":{"rendered":"https:\/\/dornsife.usc.edu\/jianfeng-zhang\/?p=863"},"modified":"2026-02-17T17:22:26","modified_gmt":"2026-02-18T01:22:26","slug":"math-505b-applied-probability-spring-2026","status":"publish","type":"post","link":"https:\/\/dornsife.usc.edu\/jianfeng-zhang\/2026\/01\/11\/math-505b-applied-probability-spring-2026\/","title":{"rendered":"Math 505B, Applied Probability, Spring 2026"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
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Math 505B, Applied Probability, Spring 2026<\/strong><\/h2>\n

 <\/p>\n

Time and location:\u00a0<\/strong>MWF 1:00pm – 1:50pm, KAP 148.<\/p>\n

Instructor:\u00a0<\/strong>Jianfeng Zhang, KAP 248E, (213)7409805<\/p>\n

Grader: <\/strong> Rundong Ding, rundongd@usc.edu<\/p>\n

Email:<\/strong>\u00a0jianfenz@usc.edu\u00a0<\/i><\/a>Homepage:<\/strong>\u00a0dornsife.usc.edu\/jianfeng-zhang\/<\/a><\/i><\/p>\n

Office hours: <\/strong>WF 9am-10:30am, in KAP 248E, \u00a0or by appointment<\/p>\n

Textbooks <\/strong>(recommended):<\/p>\n

Probability and Random Processes<\/em>, 3rd\/4th edition, by Geoffrey Grimmett and David Stirzaker<\/p>\n

Markov Chains<\/em>, by James R. Norris, Cambridge University Press<\/p>\n

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Prerequisites: <\/strong>\u00a0Math 505A (or approval by the instructor)<\/p>\n

Exam Dates:<\/strong><\/p>\n

Midterm Exam: March 13, Friday, in class<\/p>\n

Final Exam: \u00a0May 6, Wednesday, 2-4pm<\/p>\n

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Course Contents: <\/strong><\/p>\n

The course will cover the basic materials of stochastic processes, both in discrete time and in continuous time. The main topics include: Markov chains from Chapter 6; Martingales from Chapter 7 and 12; Brownian motions and stochastic calculus from Chapter 13. If time allows, we may also cover some selected topics from Chapters 8-11. A tentative list of contents is as follows:\u00a0<\/span><\/strong><\/p>\n

Chapter 0<\/strong>. Introduction<\/strong>\u00a0<\/span><\/p>\n

Chapter 1.<\/strong> Markov Chains<\/strong><\/p>\n

1.1 Markov processes<\/p>\n

1.2 Classification of states<\/p>\n

1.3 Classification of chains<\/p>\n

1.4 Stationary distributions and the limit theorem<\/p>\n

1.5 Chains with finitely many states<\/p>\n

1.6 (Continuous time) Poisson process<\/p>\n

1.7 Continuous time Markov chains<\/p>\n

Chapter 2.<\/strong> Discrete Time Martingale<\/strong><\/p>\n

2.1 Martingales<\/p>\n

2.2 Stopping times<\/p>\n

2.3 Some estimates for martingales and convergence theorems<\/p>\n

Chapter 3.<\/strong> Continuous Time Martingales and Brownian M<\/strong>otion<\/b><\/p>\n

3.1 Filtrations and continuous time processes<\/p>\n

3.2 Brownian motions<\/p>\n

3.3 Brief introduction of the Ito’s stochastic calculus\u00a0<\/span><\/p>\n

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Grading and Examination Policies <\/strong><\/p>\n

30% of the grade will be based on homework assignments, 25% on the midterm exam, and 45% on the final exam.<\/p>\n

Homework will be assigned weekly. You are encouraged to discuss homework problems with classmates. However, you are not allowed to copy other people’s work.<\/p>\n

The (50 minutes) midterm exam will be given in regular class time on\u00a0March 13, Friday<\/strong>. It will be open book, open notes, but noncooperative.<\/p>\n

The final exam will be on\u00a0May 6, Wednesday, 2-4pm, <\/strong>with the same policy as the midterm exam. The final exam will be comprehensive, but with more emphasis on the materials after the midterm.<\/p>\n

Feedback and Questions <\/strong><\/p>\n

It is extremely important for me to get feedback and questions, both inside and outside class. You are very welcome to visit me during my office hours, and\/or make appointments to see me at other time.<\/p>\n

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Statement for Students with Disabilities <\/strong><\/p>\n

USC welcomes students with disabilities into all of the University\u2019s educational programs. The Office of Student Accessibility Services<\/a> (OSAS) is responsible for the determination of appropriate accommodations for students who encounter disability-related barriers. Once a student has completed the OSAS process (registration, initial appointment, and submitted documentation) and accommodations are determined to be reasonable and appropriate, a Letter of Accommodation (LOA) will be available to generate for each course. The LOA must be given to each course instructor by the student and followed up with a discussion. This should be done as early in the semester as possible as accommodations are not retroactive. More information can be found at osas.usc.edu<\/a>. You may contact OSAS at (213) 740-0776 or via email at osasfrontdesk@usc.edu<\/a>.<\/p>\n

Statement on Academic Integrity <\/strong><\/p>\n

The University of Southern California is foremost a learning community committed to fostering successful scholars and researchers dedicated to the pursuit of knowledge and the transmission of ideas. Academic misconduct is in contrast to the university\u2019s mission to educate students through a broad array of first-rank academic, professional, and extracurricular programs and includes any act of dishonesty in the submission of academic work (either in draft or final form).<\/p>\n

This course will follow the expectations for academic integrity as stated in the USC Student Handbook<\/a>.\u00a0All students are expected to submit assignments that are original work and prepared specifically for the course\/section in this academic term. You may not submit work written by others or \u201crecycle\u201d work prepared for other courses without obtaining written permission from the instructor(s). Students suspected of engaging in academic misconduct will be reported to the Office of Academic Integrity.<\/p>\n

Other violations of academic misconduct include, but are not limited to, cheating, plagiarism, fabrication (e.g., falsifying data), knowingly assisting others in acts of academic dishonesty, and any act that gains or is intended to gain an unfair academic advantage.<\/p>\n

Academic dishonesty has a far-reaching impact and is considered a serious offense against the university. Violations will result in a grade penalty, such as a failing grade on the assignment or in the course, and disciplinary action from the university itself, such as suspension or even expulsion.<\/p>\n

For more information about academic integrity see the student handbook<\/a> or the Office of Academic Integrity\u2019s website<\/a>, and university policies on Research and Scholarship Misconduct<\/a>.<\/p>\n

Please ask your instructor if you are unsure what constitutes unauthorized assistance on an exam or assignment or what information requires citation and\/or attribution.<\/p>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":265,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-863","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"acf":[],"yoast_head":"\nMath 505B, Applied Probability, Spring 2026<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/jianfeng-zhang\/2026\/01\/11\/math-505b-applied-probability-spring-2026\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Math 505B, Applied Probability, Spring 2026 - 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