Thanks NPTEL to allow us to have the pleasure of watching Prof. V. Balakrishnan lectures. Honestly, His thinking is so clear that I want to watcth everything he has to teach.
At its heart, all this is a probabilistic attempt to predict the future. Think of it as developing a mathematical-based psychic ability. Show me the future values and I’ll show you the money; as in finding your pot of gold at the end of the stock market rainbow, for instance. Humanity doesn’t develop areas of applied mathematics, like financial engineering, just for the fun of it. This gentleman is an incredibly insightful lecturer; a pleasure to watch, as he effortlessly explains the logic and the thought process behind the math.
Thanks for the precious lecture. but it will be better if the camera is more stationary on the blackboard rather than chasing the professor all the times.
In this video at the time 38:51 respected Professor has suggested to subtract P(k, t-del(t)/j) from both side but I feel instead of this actually P(l, t-del(t)/j) has to be subtracted from both side. Anyone please confirm so that I could convince myself.
No. If u subtract P(k, t-t'/j) and divide by t-t'= del(t) then alone u ll end up as [P(k, t/j) - P(k, t-t'/j)]/del(t) and as u approach del(t) to 0 u ll end up with differential form d/dt(P(k,t/j). l is just an intermediate state and summed over. thus act as dummy variable
The trick is to remove the term with index `k` from the sum, then factor the term `P(k, t-dt | j)` (the factor is `[dt w(k|k) -1]` ), and use `sum_l P(l, dt | k) = 1`. As a side note, you can also do the whole operation between `t+dt` and `t` to avoid carying `t-dt` everywhere.
Actually the reason why Indian applied mathematics don't progress is because of such abstract presentation of the subject with unnecessary pedanticity. The subject is presented in such a way that rarely people would grasp the underlying working idea because of the steep increase in the learning curve. Compare Prof. John Tsitsiklis, MIT, lecture on Markov chains with Prof. Balakrishnan's, in three lectures Prof. Tsitsiklis not only gave a fair description of the process but also illustrated its application with examples without going into unnecessary existence theorems. It's like we do not teach our kids Peano's axioms to teach them arithmetic. My take is, if stationarity/strict stationarity is not to be discussed in details what is the necessity of teaching Kolmogorov's extension theorem that too in an introductory class on stochastic process but important topics like steady state convergence, periodicity, etc are left out? Here is the need of improving the syllabus.
This is not lecture on applied math... Its for the sake of physicist who need to develop intuition behind stochastic process and how to do it from scratch... Even as a non physicist I enjoy the way he taught here and made people to think on every steps of the procedure logically
@@pramod120895 I don't want to hurt your feelings but Prof. Balakrishnan's discourse has many technical errors. The basic error he makes here is while explaining the Kolmogorov's extension theorem. And there are lot more... . In an introductory stochastic process class one doesn't simply need to learn all that let alone learn incorrect stuff from rigorous point of view.
@@pramod120895 Incorrectness of this lecture is complete lack of rigour. Stationarity of stochastic processes is not formally expressed as P(k, t-t' | j), it's true only for stationarity in weak sense. One cannot reduce a stationarity in strong sense i.e. P(x_ti, y_t'j) = P(x_ti+τ, y_t'j+τ) ∀ τ and i, j ∈ R to P(k, t-t' | j). It is a complete distortion of definition. Also he erred by invoking the Kolmogorov Extension Theorem to explain stationarity Markov Chains when the theorem is applicable in general stochastic case. There are lots of errors so much so that people who know the subject will raise objection.
Thanks NPTEL to allow us to have the pleasure of watching Prof. V. Balakrishnan lectures. Honestly, His thinking is so clear that I want to watcth everything he has to teach.
Exactly...............
At its heart, all this is a probabilistic attempt to predict the future. Think of it as developing a mathematical-based psychic ability. Show me the future values and I’ll show you the money; as in finding your pot of gold at the end of the stock market rainbow, for instance. Humanity doesn’t develop areas of applied mathematics, like financial engineering, just for the fun of it. This gentleman is an incredibly insightful lecturer; a pleasure to watch, as he effortlessly explains the logic and the thought process behind the math.
Finally understood the essence of stochastic movement thanks!
Beautiful!
Such a boss
It took me solid 20 minutes of pause and ponder to understand how the coefficients came about.
Thanks for the precious lecture. but it will be better if the camera is more stationary on the blackboard rather than chasing the professor all the times.
well the camera movement is not a stationary process.
ikr it's really disorienting and it has been so in NPTEL lectures from this time
Next time, cameraman should fix the camera to the board
Fantastic lectures. Are there any written notes for these lectures?
👍👍
let me the professor teach QFT and particle physics.
In this video at the time 38:51 respected Professor has suggested to subtract P(k, t-del(t)/j) from both side but I feel instead of this actually P(l, t-del(t)/j) has to be subtracted from both side. Anyone please confirm so that I could convince myself.
No. If u subtract P(k, t-t'/j) and divide by t-t'= del(t) then alone u ll end up as [P(k, t/j) - P(k, t-t'/j)]/del(t) and as u approach del(t) to 0 u ll end up with differential form d/dt(P(k,t/j). l is just an intermediate state and summed over. thus act as dummy variable
Yes, it seems there is a problem. Even if we want to make the differential, somehow the intermediate state is not adding up.
The trick is to remove the term with index `k` from the sum, then factor the term `P(k, t-dt | j)` (the factor is `[dt w(k|k) -1]` ), and use `sum_l P(l, dt | k) = 1`.
As a side note, you can also do the whole operation between `t+dt` and `t` to avoid carying `t-dt` everywhere.
Could anyone suggest a book for stochastic process..?
the camera movement is stochastic
Actually the reason why Indian applied mathematics don't progress is because of such abstract presentation of the subject with unnecessary pedanticity. The subject is presented in such a way that rarely people would grasp the underlying working idea because of the steep increase in the learning curve. Compare Prof. John Tsitsiklis, MIT, lecture on Markov chains with Prof. Balakrishnan's, in three lectures Prof. Tsitsiklis not only gave a fair description of the process but also illustrated its application with examples without going into unnecessary existence theorems. It's like we do not teach our kids Peano's axioms to teach them arithmetic. My take is, if stationarity/strict stationarity is not to be discussed in details what is the necessity of teaching Kolmogorov's extension theorem that too in an introductory class on stochastic process but important topics like steady state convergence, periodicity, etc are left out? Here is the need of improving the syllabus.
This is not lecture on applied math... Its for the sake of physicist who need to develop intuition behind stochastic process and how to do it from scratch... Even as a non physicist I enjoy the way he taught here and made people to think on every steps of the procedure logically
These lectures are beautiful, most plug and chuggers, even MIT ones, don't make deep interesting discoveries
@@pramod120895 I don't want to hurt your feelings but Prof. Balakrishnan's discourse has many technical errors. The basic error he makes here is while explaining the Kolmogorov's extension theorem. And there are lot more... . In an introductory stochastic process class one doesn't simply need to learn all that let alone learn incorrect stuff from rigorous point of view.
@@RenormalizedAdvait can u pinpoint the in correctness in his lectures
@@pramod120895 Incorrectness of this lecture is complete lack of rigour. Stationarity of stochastic processes is not formally expressed as P(k, t-t' | j), it's true only for stationarity in weak sense. One cannot reduce a stationarity in strong sense i.e. P(x_ti, y_t'j) = P(x_ti+τ, y_t'j+τ) ∀ τ and i, j ∈ R to P(k, t-t' | j). It is a complete distortion of definition.
Also he erred by invoking the Kolmogorov Extension Theorem to explain stationarity Markov Chains when the theorem is applicable in general stochastic case. There are lots of errors so much so that people who know the subject will raise objection.
FAIL