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 Processes, Semigroups and
Generators 
Jan

19

Lec4: Markov Chains (MC): definitions,
transition probabilities matrices, examples

21

Lec5: MCs: classification of states,
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 Stopping
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:
Miltidimensional BM: Definition, 2D BM.

27

Lec18: BM: Variations of BM
and Extensions

Mar

2

Let19: BM: martingale methods

4

Lec20: BM:
Laplace Transform and Application in Finance (Perpetual
Warrant) 
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

Good Friday (No Lecture)

Apr

6

Lec33: DP: Integration by Parts
Formula/ Girsanov's Theorem 
8

Lec34: DP:
Applications in Finance, (B,S)Security Markets,
RiskNeutral Measure 
10

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

13

Lec36: LP:
LevyKhintchine Formula 
15

Lec37:
LP: Poisson Measure and Integral I
(Lec38 (Appendix): LevyIto Decomposition)


Enjoy the Levy Processes!
