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11 views

Weak stochastic integral

I recently encountered the following object, referred to as "weak stochastic integral" in the book of SPDE's by Prevot/Rockner [PR07]: $ \int_0^T { \langle \Psi dW(t), \Phi(t)\rangle }$ A few useful ...
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27 views

optimization problem in mathmetical finance using convex duality

I'm interested in the application of stochastic processes and stochastic calculus in mathematical finance. In my lecture I often see a certain optimization problem usually of a convex function. ...
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0answers
29 views

New stochastic calculus

I am interested in Kagi and Renko approach and hope I can use it for a random walk process. I searched for it on internet but I couldnt find any basic material to read about it. Can someone please ...
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1answer
37 views

Stochastic processes with non-zero higher order variations

I'm under the impression that how non-zero quadratic variation of the Brownian motion results in Itō's lemma or in general, the creation of the Itō's calculus. I'm also aware that stochastic integral ...
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125 views

Good books on “advanced” stochastic analysis

Any good books suggestion for studding advanced features of stochastic analysis ? Thank's in advance
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87 views

general semimartingale theory

Last semester I attended a course about stochastic calculus. There we constructed the stochastic integral with respect to continuous semimartingales. We restrict ourselves to the continuous case. ...
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1answer
959 views

Questions and Solutions in Brownian Motion and Stochastic Calculus?

I am currently studying Brownian Motion and Stochastic Calculus. I believe the best way to understand any subject well is to do as many questions as possible. Unfortunately, I haven't been able to ...
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1answer
139 views

Solving SDE's on subsets of $R^n$.

It is well-known (see for instance Oskendal's text) that if $T>0$ and $$b(\cdot,\cdot): [0,T] \times \mathbb{R}^n \rightarrow \mathbb{R}^n~~~~~~\sigma(\cdot,\cdot):[0,T] \times \mathbb{R}^n ...