# Search Results

Search type | Search syntax |
---|---|

Tags | [tag] |

Exact | "words here" |

Author |
user:1234 user:me (yours) |

Score |
score:3 (3+) score:0 (none) |

Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |

Views | views:250 |

Sections |
title:apples body:"apples oranges" |

URL | url:"*.example.com" |

Favorites |
infavorites:mine infavorites:1234 |

Status |
closed:yes duplicate:no migrated:no wiki:no |

Types |
is:question is:answer |

Exclude |
-[tag] -apples |

For more details on advanced search visit our help page |

A stochastic process is a collection of random variables usually indexed by a totally ordered set.

**2**

votes

**0**answers

If $X_t$ is a (continuous) diffusion process solving
$$
dX_t = b(t,X_t)dt + \sigma(t,X_t)dW_t
,
$$ then its infinitesimal generator, denoted by $L$ is of the form by
$$
L(f) =
b(x) \cdot \nabla_{x} f( …

asked Jan 24 by AIM_BLB

**0**

votes

**1**answer

Suppose that $\phi(t,x):[0,\infty)\times \mathbb{R}^d\rightarrow \mathbb{R}^d$ is a flow. Is it possible to extend $\phi$ to a family of stochastic flows $\{\Phi(t,x,\sigma)\}_{\sigma \in [0,1]}$ suc …

asked Feb 11 by AIM_BLB

**2**

votes

**0**answers

Intuitive Question
Suppose I'm given a set of $k$ time-series $\{X_t^1,\dots X_t^k\}$. Is there a way to determine how much of each series is dependent on the others.
Formal Question
More precis …

asked Oct 9 '16 by AIM_BLB

**1**

vote

**1**answer

If $X_t$ is a semi-martingale, $\mathfrak{F}_t$ is the $\sigma$-field generated by $X_t$ and $L^2(Pred)$ is the set of all $\mathfrak{F}_t$-predictible processes. Then is it true that:
$$
\mathfrak{G …

asked Nov 3 '16 by AIM_BLB

**0**

votes

**0**answers

The set $\mathscr{S}$, of semi-martingales is a topological vector space under the Emery topology on the space of semi-martingales. There has been some recent research on closures in this topology (f …

asked Oct 21 '18 by AIM_BLB

**2**

votes

**1**answer

I know there are Itô formulas for cylindrical Brownian motions with values in a Hilbert space and Itô formulas for Lévy processes in $\mathbb{R}^d$. My question is:
does there exist an Itô formula fo …

asked Sep 3 '16 by AIM_BLB

**0**

votes

**0**answers

There are a variety of control problems for controlled diffusions $X_t^u$, with the terminal cost given by
$$
J(u)\triangleq \mathbb{E}\left[g(X_T,u)+\int_0^t h(X_t,u_t)ds\right],
$$
function $g$ and …

asked Dec 21 '18 by AIM_BLB

**1**

vote

**0**answers

Is there any literature dealing with a stochastic control problem whose cost-functional $J_t$ is stochastic also?
That is, let $X_t^u$ is the solution to a controlled SDE
$$
dX_t = \mu(t,u_t,X_t^u)dt …

asked Jun 21 '17 by AIM_BLB

**0**

votes

**2**answers

Is there an extension of Ito's Lemma where $X_t$ is a semi-martingale and $f:\mathbb{R}^d \rightarrow \mathbb{R}$ is a function which is not smooth?
I've been looking but have not found much, any ref …

asked Jan 11 '17 by AIM_BLB

**3**

votes

**1**answer

Can every càdlàg semi-martingale be written as a sequence of diffusions? That is, is the set of continuous semi-martingales dense in some Skorohod space?

asked Jun 6 '17 by AIM_BLB

**-1**

votes

**1**answer

Background
I've been reading this article and it keeps referring to "Grigelionis processes", which apparently generalize Levy processes. However the paper does not define these object clearly and …

asked Jan 23 '16 by AIM_BLB

**1**

vote

**1**answer

I'm fairly familiar with the literature dealing with convergence of SDEs in $\mathbb{R}^d$ but recently I've needed to use extended results dealing with convergence of SDEs in Hilbert Spaces. However …

asked Aug 19 '16 by AIM_BLB

**1**

vote

**1**answer

Motivation
Then the usual stochastic filtering problem says that:
$$
\operatorname{argmin}_{Z \in L^2(\mathscr{G}_t)}\,\mathbb{E}[(Y_t-Z_t)^2],
$$
where $\mathscr{G}_t$ is the $\sigma$-algebra genera …

asked Sep 29 '16 by AIM_BLB

**3**

votes

**1**answer

Suppose I have signal process $\lambda_t$ following the dynamics
\begin{equation}
\begin{aligned}
\zeta_t&=\mu^{\zeta}(t,{\zeta}_t)dt+\sigma^{\zeta}(t,{\zeta}_t)dW^{\zeta}_t\\
\xi_t&=\mu^{\xi}(t,\xi_t …

asked Jul 10 '17 by AIM_BLB

**3**

votes

**0**answers

Suppose that $\{a_n(x)\}_{n \in \mathbb{N}}$ is a sequence of real-valued Lipschitz functions with domain $\mathbb{R}^d$, which converges $m$-a.e. to a Lipschitz function $a$. Suppose that $b$ is a L …

asked Sep 22 '18 by AIM_BLB