Month

Day

Monday

Day

Wednesday

Day

Friday

Jan

12

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

14

Lec2:
Elements of stochastic processes: classification, definition

16

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

Jan

19

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

21

Lec5:
MCs: basic
limit theorem of Markov chains

23

Lec6:
MC: finite
state continuous time MC

Jan

26

Lec7:
Renewal
Processes(RP): definition, examples

28

Lec8: RP: Renewal
Equations

30

Lec9:
RP:
Renewal Theorems 
Feb

2

Lec10:
RP: Variations of RP (Delayed, Stationary, CLT,etc.) 
4

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

6

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

9

Lec13: Martingales: The Optional Sampling
Theorem (OST); Applications of OST 
11

Lec14:
Martingales: applications to discretetime (B,S)security markets
(finance) 
13

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

16

Reading Week (No Lectures) 
18

Reading Week (No Lectures) 
20

Reading Week (No Lectures) 
Feb

23

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

25

Lec17: BM: Variations of BM and Extentions

27

Lec18:
BM: martingale methods 
Mar

2

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

4

Lec20:
Miltidimensional BM: Definition, 2D BM.

6

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

9

Lec22: BP: generating function relation
for BP

11

Lec23:
BP: extinction probabilities, martingale properties

13

Lec24:
BP: continuoustime,
extinction probabilities

Mar

16

Lec25:
Stationary Processes(SP): definition, examples 
18

Lec26:
SP: Mean Square Error Prediction

20

Lec27:
SP: The Prediction
Theorems and Examples 
Mar

23

Lec28:
SP: Ergodic Theory
for SP 
25

Lec29:
Diffusion Processes (DP): definition, examples 
27

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

30

Lec31:
DP:
Existence and Uniqueness Theorem /Ito Formula 
1

Lec32:
DP: Ito formula /Integration by Parts Formula

3

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

6

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

8

Lec35:
Levy Processes
(LP):
definition, examples, infinite
divisibility 
10

Good
Friday (No Lectures) 
Apr

13

Lec36:
LP: LevyKhintchine
Formula 
15

Lec37:
LP: Poisson Measure and
Integral

17

Lec38:
LP: LevyIto Decomposition/Applications
(finance) 