Month

Day

Monday
(11am)

Day

Wednesday
(8am)

Day

Wednesday
(11am)

Jan

10

Lec1:
Introduction:
Course outline; Elements of stochastic
processes: review of basic terminology, two simple examples

12

Lec2:
Elements of stochastic processes: classification, definition

12

Lec3:
Markov Chains (MC): examples, transition probabilities

Jan

17

Lec4:
MC:
transition probabilities matrices,
classification of states, recurrence

19

Lec5:
MCs: basic
limit theorem of Markov chains

29

Lec6:
MC: finite
state continuous time MC

Jan

24

Lec7:
Renewal
Processes(RP): definition, examples

26

Lec8: RP: Renewal
Equations

26

Lec9:
RP:
Renewal Theorems 
JanFeb

31

Lec10:
RP: Variations of RP
(Delayed, Stationary, CLT,etc.)

2

Lec11:
Martingales: definition,
examples, supermartingales and
submartingales (discrete time)

2

Lec12:
Martingales (sub and supermartingales): continuous time 
Feb

7

Lec13: Martingales: The Optional Sampling
Theorem (OST); Applications of OST 
9

Lec14:
Martingales: applications to discretetime (B,S)security markets
(finance) 
9

Lec15:
Brownian Motion (BM): background, joint probabilities 
Feb

14

Lec16:
BM: continuity of paths,
reflection principle and the
maximum value

16

Lec17: BM: Variations of BM and Extentions

16

Lec18: BM: martingale methods 
Feb

21

Reading Week (No Lectures)

23

Reading
Week (No Lectures)

23

Reading
Week (No Lectures)

FebMar

28

Let19: BM: Laplace Transform and
Application in Finance
(Perpetual Warrant)

2

Lec20:
Miltidimensional BM:
Definition, 2D BM.

2

Lec21:
Branching Processes
(BP): Examples, pure birth, birth and death processes 
Mar

7

Lec22: BP: generating function relation
for BP

9

Lec23:
BP: extinction probabilities, martingale properties

9

Lec24:
BP: continuoustime,
extinction probabilities

Mar

14

Lec25:
Stationary Processes(SP): definition, examples 
16

Lec26:
SP: Mean Square Error
Prediction

16

Lec27:
SP: The Prediction
Theorems and Examples 
Mar

21

Lec28:
SP: Ergodic Theory
for SP 
23

Lec29:
Diffusion
Processes (DP): definition, examples 
23

Lec30:
DP:
definition,
examples II /Existence and Uniqueness Theorem 
MarApr

28

Lec31:
DP:
Existence and Uniqueness Theorem /Ito Formula 
30

Lec32:
DP: Ito formula /Integration by Parts Formula

30

Lec33:
DP: Integration by
Parts Formula/ Girsanov's Theorem

Apr

4

Lec34:
DP: Applications in
Finance, (B,S)Security Markets, RiskNeutral Measure

6

Lec35:
Levy Processes
(LP):
definition, examples, infinite
divisibility 
6

Lec36:
LP: LevyKhintchine
Formula 
Apr

11

Lec37:
LP: Poisson Measure and
Integral I 
13

Lec38:
LP: Poisson Measure and
Integral II 
13

Lec39:
LP: LevyIto
Decomposition/Applications
(finance) 