Stochastic process

[CGiuliano]

Ok, so next semester I'm going to be taking stochastic process, and my school offers a few different options. Please advise me on which to take, or what the major difference might be.

Thanks.

One Semester -- Math Department -- Stochastic Process
MATH 4740 Stochastic Processes (MQR)
Spring. 4 credits. Prerequisites: MATH 4710, BTRY 4080, ORIE 3600, or ECON 3190 and some knowledge of matrices (multiplication and inverses).
A one-semester introduction to stochastic processes which develops the theory together with applications. Markov chains in discrete and continuous time, Poisson processes, queuing theory, martingales, Brownian motion, and option pricing.

Engineering Stochastic Process Sequence
ORIE 3510 Introductory Engineering Stochastic Processes I
Spring and summer. 4 credits. Prerequisite: grade of C– or better in ORIE 3500 or equivalent.
Uses basic concepts and techniques of random processes to construct models for a variety of problems of practical interest. Topics include the Poisson process, Markov chains, renewal theory, models for queuing, and reliability.

ORIE 4520 Introductory Engineering Stochastic Processes II
Spring. 4 credits. Prerequisite: ORIE 3510 or equivalent.
Topics include stationary processes, martingales, random walks, and gambler’s ruin problems, processes with stationary independent increments, Brownian motion and other cases, branching processes, renewal and Markov-renewal processes, reliability theory, Markov decision processes, optimal stopping, statistical inference from stochastic models, and stochastic comparison methods for probability models. Applications to population growth, spread of epidemics, and other models.

Graduate Stochastic Calculus Sequence -- In M.eng curriculum
ORIE 5600 Financial Engineering with Stochastic Calculus I
Fall. 4 credits. Prerequisite: knowledge of probability at level of ORIE 3500.
Introduction to continuous-time models of financial engineering and the mathematical tools required to use them, starting with the Black-Scholes model. Driven by the problem of derivative security pricing and hedging in this model, the course develops a practical knowledge of stochastic calculus from an elementary standpoint, covering topics including Brownian motion, martingales, the Ito formula, the Feynman-Kac formula, and Girsanov transformations.

ORIE 5610 Financial Engineering with Stochastic Calculus II
Spring. 4 credits. Prerequisite: ORIE 5600.
Building on the foundation established in ORIE 5600, this course presents no-arbitrage theories of complete markets, including models for equities, foreign exchange, and fixed-income securities, in relation to the main problems of financial engineering: pricing and hedging of derivative securities, portfolio optimization, and risk management. Other topics include model calibration and incomplete markets.

 

[DanM]

I'm actually going to be taking a course that's very similar to the first one you posted.

 

[IlyaKEightSix]

Interesting in that Lehigh had much the same sort of option. In sophomore year, I took the equivalent of the first. That said, are you telling me that you get to take stoch. calc as an undergrad?

Lucky bastard -.-...

 

[DanM]

Interesting in that Lehigh had much the same sort of option. In sophomore year, I took the equivalent of the first. That said, are you telling me that you get to take stoch. calc as an undergrad?

Lucky bastard -.-...

We have a stochastic calculus for finance course (graduate) here that we can take in undergrad, too.

It's pretty sweet.

 

[CGiuliano]

They let us register for any classes we want. Literally. Regardless of if you have the prerequisites, i.e. a history major can register for quantum mechanics 2 with no background in physics whatsoever. The only exception to this rule, is if the professor puts a block on registration. In this case you have to get permission first, but this is usually for over filled freshman classes.

That being said, I'm al ready taking a graduate stats class, so it may not be smart to pile on graduate stochastic calculus. How difficult is the course?

 

[IlyaKEightSix]

What kind of stats course? I'm in the stats masters here at Rutgers. It bores me. Basically, I did more work for my quant opt course in Lehigh than I'm doing for these 12 credits combined.

Now this may very well change towards the end because 3 classes have a final individual project and one class has a final worth 50% (and a midterm worth 50%), but it's literally my undergraduate probability course all over again.

I can't say how hard or easy Cornell classes are. Clearly, they vetted out the best of you people. That said, graduate classes (at least MS level), in my mind, unless they're taught by an MIT girl who has a much different interpretation of easy, require less work than undergrad courses because they don't chase you with homework assignments as much.

Furthermore, from my mixed grad experience in Lehigh, they were some of my best grades.

For an OR guy, the worst you have to fear from a stats class is an obnoxiously arbitrary software package or sheer boredom. I'd say go for it. You're only in college once. Get everything you can. If you even get so much as a 3.3, employers will say your GPA is solid and strong (at least that's what Lehigh alumni tell me =X), considering you're an engineer.

 

[financeguy]

I would take the MATH 4740 course first.. it's the standard first course in stochastic processes. Afterwards go through the graduate stochastic sequence - looks like some great applications to financial engineering. I would just be hesitant to take a course involving stochastic calculus before you develop the basics.

 

[CGiuliano]

Here are the stats classes. It's just a normal intro/grad sequence, but I was told that it is doable for undergrads, and I've heard it is the "best" stats option. My advisor said I may even be at an advantage because most of the grad students taking it do not have an extensive math background.

Oh, yeah ignore that prerequisite. The online system doesn't discriminate against undergrads. :D

BTRY 6010 Statistical Methods I (also ILRST 6100)
Fall. 4 credits. Prerequisite: graduate standing.
Develops and uses statistical methods to analyze data arising from a wide variety of applications. Topics include descriptive statistics, point and interval estimation, hypothesis testing, inference for a single population, comparisons between two populations, one- and two-way analysis of variance, comparisons among population means, analysis of categorical data, and correlation and regression analysis. Introduces interactive computing through statistical software. Emphasizes basic principles and criteria for selection of statistical techniques.

BTRY 6020 Statistical Methods II
Spring. 4 credits. Prerequisite: graduate standing; BTRY 6010 or equivalent.
Continuation of BTRY 6010. Emphasizes the use of multiple regression analysis, analysis of variance, and related techniques to analyze data in a variety of situations. Topics include an introduction to data collection techniques; least squares estimation; multiple regression; model selection techniques; detection of influential points, goodness-of-fit criteria; principles of experimental design; analysis of variance for a number of designs, including multi-way factorial, nested, and split plot designs; comparing two or more regression lines; and analysis of covariance. Emphasizes appropriate design of studies before data collection, and the appropriate application and interpretation of statistical techniques. Practical applications are implemented using a modern, widely available statistical package.

 

[IlyaKEightSix]

I don't want to underestimate Cornell graduate course professors, because if anyone, they can make a simple course challenging, but just looking at that material...

A strong Cornell IEOR student should be able to burn those courses up half-asleep.

 

[CGiuliano]

hmmm...

What should I be looking for in a stats sequence?

 

[financeguy]

That sounds fine for a stats sequence.