Top Tweets for #stochasticCalculus
Il valore atteso dell'integrale di Itô di un processo adattato sufficientemente regolare è 0.
Lo si può verificare numericamente generando migliaia di traiettorie del processo di Wiener e calcolandone gli integrali per una funzione scelta.
#StochasticCalculus #MATLAB
@mathelirium That +dt in Itô's formula for B_t² isn't just technical. It's the deterministic shadow of wild noise that refuses to vanish—a primitive correction letting calculus survive chaos.
Without it, paths drift away. Life thrives on that very edge.
#StochasticCalculus #ItoFormula
The gap is where the money is. And where the blowups live.
#usefulwrongmoodels
#QuantitativeFinance #StochasticCalculus #Models #trading
I just launched "Unlocking Stochastic Calculus: Episode 1 of 6"! Breaking down complex math with 3Blue1Brown-style visuals. From basics to finance modeling, 2 vids/week. Check it out: https://t.co/iMfUL1dMzo #QuantFinance #StochasticCalculus
Unlock the world of stochastic calculus and mathematical finance! 📊 Learn the fundamentals of Itô integrals, stochastic differential equations, and the Black-Scholes model.
Check it out on Amazon: https://t.co/0r0s9Wt3Xa
#StochasticCalculus #MathFinance #FinanceBooks
Master stochastic calculus with ease! 👨🎓 This problem-solution book covers applications in finance, biology, and more. Ideal for students, researchers, and instructors seeking a deeper understanding of probability and stochastic processes. 📚
#stochasticcalculus #mathematics
Continue your professional education with Quantopian's online Stochastic Calculus for Finance course, taught by Indiana University Professor, Esfan Haghverdi.
Course starts August 5, registration open now: https://t.co/6MA72kj8oq
#calculus #finance #stochasticcalculus
Uncover the fundamentals of Stochastic Calculus with an introductory approach that mirrors deterministic Calculus. Easy to follow and perfect for students and newcomers to the field! 📚
Read the free sample chapter now https://t.co/MY3DHCXSNO
#StochasticCalculus #Mathematics
Unlock the secrets of stochastic calculus! Discover how it applies to finance, biology & engineering. 💡
Read a FREE chapter now & dive into stochastic processes! https://t.co/UtrdjdhvWT
#StochasticCalculus #Mathematic
in the memory of dr. kiyosi itô. 👾🇯🇵🇺🇸🇹🇷
https://t.co/ER48EtjFsg
cc @KyotoU_News, @UniOfTokyo, @BrownUniversity ❤️
#itocalculus #stochasticcalculus #taylorswiftseries ;)
and ofc cc her majesty @taylorswift13 😘
I was reviewing my #StochasticCalculus notes from the old days and realized how not easy was at that time to build a proper intuition of what the fundamental concepts of probability space, filtrations, ... meant
At some point, I got an imho decent analogy that could be worth sharing as a random Saturday post
Let's start from the formal definition of #probability which is the well-known tuple (\Omega, \mathcal{F}, P) and we all know the formal definitions of these symbols
The analogy is
- \Omega is the set of "letters" so basically an alphabet
- \mathcal{F} i.e. the Sigma Algebra is a set of "sentences" which is possible to express which is possible to express with this alphabet
- P is some measure associated with these sentences
This already draws a connection between the Sigma Algebra and some "Information" that can be expressed in this "space" and
a measure for this information and this brings us closer to the Information Theory as well
How can this be connected to probability theory?
Let's think of these "sentences" i.e. the Sigma Algebra elements, as expressing "events" so P can be a measure of the probability for each of these events to happen
Now let's think of the time
This representation is "static" meaning there is no notion of time and therefore all the 3 components of this space do not change
Adding the notion of time makes sense to apply this theory to the real-world and therefore to be able to study how information evolves with time and this leads us to Martingale Theory
Of course, for consistency across different time points, we want to keep the \Omega alphabet and the P measure static, so what changes is the Sigma Algebra: as time goes on, the number of "sentences" or "events" we are considering changes
So the Sigma Algebra is the "memory" of our system, it records the passed "sentences" or "events"
The Filtration in the Martingale Theory is the Sigma Algebra at a certain point in time and since by construction this S.A. is such that it includes all the previous (i.e. back in time) S.A.s then it can be thought of as an "infinite memory" recording more and more "events"
#StochasticCalculus notes: Criteria for Poisson Point Processes
Main result: Any simple point process satisfying the independent increments property is Poisson.
This justifies their use in many situations (both theoretical and practical).
https://t.co/XiAcDMMSXB
New almostsure blog post: Model-Independent discrete barrier adjustments.
When monitoring a continuous barrier, but sample discretely, adjustments are required for good convergence.
This looks at how it can be done in a generic way
#StochasticCalculus
https://t.co/x01yhzsHdo
#StochasticCalculus notes: Poisson point processes
https://t.co/lg34kPKOAN
#StochasticCalculus notes: The Kolmogorov continuity theorem
https://t.co/DGz9eFf26r
New almostsure blog post!
This looks at how you can adjust the values of a discretely sampled process in order to accurately monitor a continuous barrier condition.
#StochasticCalculus
https://t.co/OZcYnkQq67
We look forward to new exciting collaborations & papers emerging from our ELLIS/@ai_elise workshop ending today - an intense exchange on #StochasticCalculus, #StatisticalPhysics & #ML with passionate European scientists that we plan to repeat next year!
https://t.co/FC3XBZP4wi
@iteacha ผมก็เคยคิดว่า Math Finance มันจะเบาหน่อย จนมาเจอ #stochasticCalculus #ConditionalExpectation #Filtration #StopingTime #StochasticOptimization 😂😂😂
#StochasticCalculus Notes: Brownian Excursions
https://t.co/wAgf1DSHcr
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