The stochastic-calculus tag has no wiki summary.

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### Systematization of deterministic and stochastic integrals

With this question I try to build up a systematization of different kinds of integrals. The following table differentiates between deterministic and stochastic integrals, the summation processes ...

**16**

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**5**answers

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### Brownian motion and spheres

Consider a Brownian motion on $[0;1]$. A (finite) discrete approximation of this Brownian motion consists of $N$ iid Gaussian random variables $\Delta W_i$ of variance $\frac{1}{N}$:
$$ ...

**9**

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**2**answers

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### Convergence and non-convergence of left-point and mid-point Riemann sums

In standard calculus it is a well known fact that left-point and mid-point Riemann sums do become equal in the limit. When it comes to stochastic integration this is no longer the case. Taking the ...

**13**

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**2**answers

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### Big Picture: What is the connection of Malliavin calculus with differential geometry?

I know that Paul Malliavin was heavily influenced by ideas from differential geometry while developing his calculus on Wiener space. But what are the concrete analogies between both areas of ...

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### Discrete version of Ito's lemma

Could anyone give me some references where I could find
(a) discrete version(s) of Ito's lemma
(b) a proof how it converges to the continuous form in the limit
(c) its usage within stochastic ...

**2**

votes

**1**answer

324 views

### Moment Generating Function: Pulling a term out of k-times differentiation

In Wiersema: Brownian Motion Calculus on p. 205 (in an Annex on Moment Generating Functions (mgf)) the following equation is being presented $${d^k \over d\theta^k} \left ({1\over ...

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**2**answers

494 views

### Exploding Levy processes

Hi,
probably this is a fairly newbie question, but is it possible that the a generic Levy process explodes (i.e. tends to infinity for finite time t with positive probability)? If yes, could you ...

**1**

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**1**answer

250 views

### Extension of some feature of SDE Ornstein-Uhlenbeck type

Hi everyone,
I am looking for some ideas (or references) in order to get an explicit SDE (if it exists) which would have a stylised property extending in some sense the mean-reversion property of SDE ...

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**2**answers

294 views

### Units in Ornstein-Uhlenbeck(OU) process

Take an OU process characterized by
X(0) = x
dX(t) = - a X(t) dt + b dW(t)
where a,b >0. The parameter a is usually interpreted a dissipative term, and b is a ...

**10**

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**2**answers

522 views

### Inequality in Gaussian space — possibly provable by rearrangement?

The following problem arose for my collaborators and me when studying the computational complexity of the Maximum-Cut problem.
Let $f : \mathbb{R} \to \mathbb{R}$ be an odd function. Let $\rho \in ...

**1**

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**4**answers

369 views

### CAS for finding closed form solutions to PDEs and SDEs?

Are there any specialized Computer Algebra Systems (or packages for these) for finding closed form solutions to
a) partial differential equations,
b) stochastic differential equations?
If yes, what ...

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467 views

### maximizing function (stochastic calculus)

S is a price process which follows Geometric Brownian motion with no drift:
dS=S*vol*dW, vol=const., W is a Wiener process.
Define the following ratio: R=E[Max(f(S)-S(T),0)]/E[f(S)], where S(T) is ...