Thin points of certain Markov processes with jumps
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Title 
Thin points of certain Markov processes with jumps

Title of Series  
Part Number 
4

Number of Parts 
17

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License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
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Publisher 

Release Date 
2016

Language 
English

Content Metadata
Subject Area  
Abstract 
A point in the state space of a stochastic process is called “thin” if the associated occupation measure of the ball centered at this point is exceptionally small. We consider in this talk the Hausdorff dimension of thin points of a class of Markov processes with jumps. This is a joint work with Stéphane Seuret.

00:00
Point (geometry)
Stochastic process
Multiplication sign
Process (computing)
Theory of relativity
Multiplication sign
Interior (topology)
Dimensional analysis
Exponentiation
Continuous function
Regular graph
Limit (category theory)
Dimensional analysis
Numerical analysis
Category of being
Regular graph
Computer animation
Causality
Absolute value
Musical ensemble
Analytic continuation
Local ring
Position operator
Social class
03:01
Logical constant
Fractal
Metric system
Multiplication sign
Firstorder logic
Dimensional analysis
Brownian motion
Measurement
Order (biology)
Estimator
Casting (performing arts)
Different (Kate Ryan album)
Thermal fluctuations
Matrix (mathematics)
Hausdorff dimension
Series (mathematics)
LipschitzStetigkeit
Local ring
Multiplication
Descriptive statistics
Area
Taylor series
Potenz <Mathematik>
Process (computing)
Point (geometry)
Mass
Translation (relic)
Measurement
Category of being
Proof theory
Arithmetic mean
Oval
Order (biology)
Different (Kate Ryan album)
Mathematical singularity
Theorem
Resultant
Point (geometry)
Spectrum (functional analysis)
Random number
Functional (mathematics)
Process (computing)
Translation (relic)
Limit (category theory)
Mathematical analysis
Regular graph
Inequality (mathematics)
Power (physics)
Frequency
Regular graph
Cantor set
Spacetime
Poisson process
Set theory
Condition number
Motif (narrative)
Multiplication sign
Time zone
Focus (optics)
Scaling (geometry)
Weight
Fractal
Physical law
Exponentiation
Expression
Projective plane
Mathematical analysis
Limit (category theory)
Hierarchy
Inequality (mathematics)
Markov chain
Hausdorff space
Computer animation
Estimation
Logic
Function (mathematics)
Set theory
Hydraulic jump
Local ring
Spectrum (functional analysis)
12:15
Supremum
Scaling (geometry)
Process (computing)
Logarithm
Propositional formula
Firstorder logic
Inequality (mathematics)
Power (physics)
Estimator
Computer animation
Estimation
Uniformer Raum
Hydraulic jump
13:09
Supremum
Computer animation
Estimation
Logarithm
Chemical equation
Propositional formula
Hydraulic jump
Inequality (mathematics)
13:29
Spectrum (functional analysis)
Logarithm
Multiplication sign
Analogy
Firstorder logic
Infinity
Regular graph
Roundness (object)
Analogy
Cantor set
Hausdorff dimension
Energy level
Spacetime
Configuration space
Poisson process
Set theory
Supremum
Scale (map)
Scaling (geometry)
Matching (graph theory)
Point (geometry)
Physical law
Mathematical analysis
Curve
Propositional formula
Staff (military)
Inequality (mathematics)
Computer animation
Doubling the cube
Estimation
Order (biology)
Mathematical singularity
Theorem
Configuration space
Set theory
Hydraulic jump
Marginal distribution
Resultant
Superposition principle
Directed graph
15:43
Voting
Meeting/Interview
Mass
00:02
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03:02
L give some examples the 1st example most interesting opposite can most interesting on burning motion it started this as it is now well it has been spending so many consider the local conditions this summer local time under a new mission 1 does exist and the higher dimensions the run motions and men's there's not a lot times when we consider local dimensions as adamant as the isolated up as defined in the last quarter some Protestant platter and consider have has proved that for all the points in support of this matter um running motion has local dimension to as such postings 1st the delineates the limit Lovelock limited doesn't is the 2nd thing is that for all .period the the regularity exponent of Asia is the same for all the texts so full the full of another kind the protease is a special case of process on others possibly process for example increasing stable in the process also calls pollinators office they was monitors we can also considers expression to occupation Maris local dimension of In this case not for all acts the support but for me almost every point support this is a result when Qatar India late nighties so does their interviews express exceptional SES exceptional .period so a quick answer is yes and talk about this later on the Net as just mentioned not a related question the full running motion hiring nations that don't have look at times but under the local dimension is he said is is is a constant for the point but we can consider some summer some fluctuation for the regularity of this matter uh This Modern Love erased some earlier make order so this is this is the work in the in the early after 2 solid the frequency a check paper by the new powers Rosen's between OK To the framework is the idea that I could adopt to consider his problem is a Somali fractal analysis and they got the best and the goal of this of this framework is to distinguish different local the area of the of the of the mayor consider measure of this bad description of a set points where but given regularity exponents starts with a given Powell age this quite so that the the definition would make sense always made sense is the opera local dimension where are you instead of taking them intimate taking this mindset for this long logic quantity we can always welcome come because we can also defined as lower local dimension which is only the beginning here under the American we call it a local image OK so the definition of this summer 1 of you will recall opera motif fractal special is matching 2 after associated each value of age possible age Powell too the .period dimension of this that was set for this regularity exponent but it's a lot measures just OK is a byword a is describes the whole thing of setting up the new matrix based in all this is the right notion in this contacts and the many orders and that but we can also consider for example packing dimensions of this kind of stuff look at so finally what is called .period the same .period recorded full of stable born in Asia full New almost every point that this horrible this also In this case the power law exists the limit is used for almost every point and but there are many other points we have another the tolerable With meager excellent age In this case are power to age is much smaller 2 that 1 so we call it in this case we call this the .period acts assumed .period 1 clarinetist proof that the host of dimensional 7 points misgiving regularity age Is this function so if I joint picture Of these this spectrum only lenders this is the host of the National Theatre the SAT insists that all possible value of age and other valuables Laura than to all lost more than all of our if as the host of this all simple empties can this offer corresponds to the host of the mention of the top of the range of stable so with to monitor just that give a few words on the process started the so the goal is to move to this crime scene .period care of the author John effusions junking Estes by using the notions of someone announces this is the kind of different difficulty differences stopped me on the phone for this kind of more general market processing of stationary increment of the business of being the difference between prices are stunning it also went the definition of the definition of this kind of process given by best introduced as in the late eighties and this is a market process was generate from this kind we remarked that if they is a constant function lyrics ,comma what we call off for stable despite nature of costly here we only keep the reality of the year and the large the La drafted does not influence the depressed the the simple past properties of a process what is more it OK so that as the 1st
10:10
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12:17
case estimated is is the following if we consider increment this is not exactly the increment of our process and but that increment truncated large nigger nigger and 2 near under then the the the the planning firm and power to 1 lower Delta Is a truncated or large amounts officer of a certain scale then we have this uniform control for the uniform control for increment of the process and a lotta Johnson's on a much smaller to control once we have this we can kill good estimate for this
13:05
making good afternoon for the for the increment so did the other mission is the following full
13:10
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13:21
total incremental this among India's that there's has some large discussed more urgent that because the
13:30
this margin documentation only gives this order under this is the
13:36
big order so that definitely there some large round for our
13:41
conclusion is that the US to Laura Johnson said time t I said such that and for every empty assess the should satisfied as foreign controls configuration he signed it look so if we all this kind of double John configuration let me when we did for the for the for the for the for the population from the population that can be considered at the scale of the plant the increment of the the the intervals Miss this kind of configuration under can by considering his descendants also consider all we also truth to cheat on his stomach on configuration will get us out of freckles have and this is where given enough about the this .period remind that we do not want to computer desk cost mission the only effective wanted considered that the set of acts such as takes this is this regularity age so that there's still some staff from time to space but in this case we have with the women need now is an analog of mission doubling serum fulfill brand motion OK law analysis must win was not going to talk about it it is it concerns the construction consensus is that this on levels and the singularity so the result is following the opera multifront respectful of this matter Is this the source of the infection is of running matching enriches the superposition of the of all this kind of this kind of curves gives also run in front of the securitization that's not
15:52
how you think dedicated status to morning Mass songcraft thank you you hear them