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Apr
18
comment Further Reading on Stochastic Calculus/Analysis
Yes, that is the book. Schilling has another book on Brownian Motion, which is essentially a guide to stochastic calculus. Also, Schilling provides solution manuals (to the exercises contained in his books) on his website, somewhere.. They are quite easily accessible.
Apr
18
comment Further Reading on Stochastic Calculus/Analysis
It depends on what you define as 'calculus'. A stochastic calculus can be defined, simply speaking, as the useful tools and results that follow given a definition of a stochastic integral. In this sense, Malliavin calculus is different to Ito calculus because the former operates under the Skohorod integral whilst the latter operates under the Ito integral. It can be shown that sometimes the Skohorod integral and Ito integral coincide and have the same value, therefore Malliavin calculus and Ito calculus are actually connected to each other!
Apr
12
comment One stochastic integrability problem
Additionally, a symbol A can be said to be well defined if it exists and is unique and satisfies some desired properties. Sometimes authors mean 'well defined' to be purely that A is finite. Sometimes however they mean that it exists, is unique, satisfies many properties, etc. Can you paste the link to the lecture notes?
Apr
12
answered Further Reading on Stochastic Calculus/Analysis
Apr
12
awarded  Citizen Patrol
Apr
5
answered Stochastic Differential Equations - A Few General Questions
Mar
21
comment Explanation of a stochastic process
From which book did you get this quote from? That notation for the expectation operator is quite bizarre but maybe it makes sense in the context of the notation that is used in that book/
Mar
21
comment Radon-Nikodym Derivatives between Ito Processes
And why would anyone want to apply a result twice when once is sufficient? That is very, very confusing to me.
Mar
21
answered Radon-Nikodym Derivatives between Ito Processes
Mar
5
comment What are some areas of research/industry involving stochastic processes that aren't finance-related?
Do you know how probability theory was invented?
Mar
5
answered What are some areas of research/industry involving stochastic processes that aren't finance-related?
Mar
1
comment Differential of stochastic term
Fantastic answer!
Feb
27
comment Why isn't Volterra's function Riemann integrable?
You do not need to know measure theory to understand the Lebesgue criterion regarding Riemann integrablity.
Feb
26
comment Importance of set theory
Hint: How do you define a number?
Feb
26
comment Have there been any attempts to unify statistics and decision theory into a single framework that refrains from estimating probabilities?
I think a lot of statisticians would give you lengthy stares after your summary of what statistics is about. Indeed, you are off the mark! Have you read a book on decision theory before?
Feb
26
comment Stochastic Processes Solution manuals.
Adding to Sez's input, one should note that anything written by Schilling is very solid - he has another text on measure theory that is a great read.
Feb
26
answered when does one use the word 'fact' in mathematics
Feb
13
comment Book request: Mathematical Finance, Stochastic PDEs
Actually, Revuz-Yor was the introductory book I used to learn meagre sets. I couldn't be bothered to look back in some of the more complicated books or probability journals - so just looked at that book and picked it up from there. It is an excellent introduction to stochastic analysis if you have very good knowledge of measure theory!
Feb
13
answered Book request: Mathematical Finance, Stochastic PDEs
Feb
8
comment Two stochastic processes with the same distribution inducing different measures
Apologies for the long wait - and you may no longer be interested in this question but I have looked at Stroock's book again and exercises 4.1.9, 4.1.10 and 4.1.11 explain why and give such an example. I am happy (although it will be torturous) to construct such an example and to explain Stroock's choice.