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Eigenvalues of the Laguerre Process as Non-Colliding Squared Bessel Processes
Wishart and Laguerre ensembles and processes eigenvalues as diffusions non-colliding squared Bessel processes
2009/5/4
Let A(t) be an n-times-p matrix with independent standard complex Brownian entries and set M(t)=A(t)*A(t). This is a process version of the Laguerre ensemble and as such we shall refer to it as the La...
Kendall's identity for the first crossing time revisited
skip-free Levy process first crossing time change of measure
2009/5/4
We give a new relatively compact proof of the famous identity for the distribution of the first hitting time of a linear boundary by a skip-free process with stationary independent increments. The pro...
How to Combine Fast Heuristic Markov Chain Monte Carlo with Slow Exact Sampling
Confidence interval Exact sampling Markov Chain Monte Carlo
2009/5/4
Given a probability law $pi$ on a set S and a function $g : S rightarrow R$, suppose one wants to estimate the mean $bar{g} = int g dpi$. The Markov Chain Monte Carlo method consists of inventing and ...
A Note on Talagrand's Concentration Inequality
Concentration of measure empirical processes
2009/5/4
In this paper we revisit Talagrand's proof of concentration inequality for empirical processes. We give a different proof of the main technical lemma that guarantees the existence of a certain kernel....
Donsker-Type Theorem for BSDEs
backward stochastic differential equation(BSDE) stability of BSDEs weak convergence of filtrations
2009/5/4
This paper is devoted to the proof of Donsker's theorem for backward stochastic differential equations (BSDEs for short). The main objective is to give a simple method to discretize in time a BSDE. Ou...
Almost Sure Stability of Linear Ito-Volterra Equations with Damped Stochastic Perturbations
stochastic functional-dierential equations Ito-Volterra equations uniform asymptotic stability pathwise stability simulated annealing
2009/4/29
In this paper we study the a.s. convergence of all solutions of the It^{o}-Volterra equation [ dX(t) = (AX(t) + int_{0}^{t} K(t-s)X(s),ds),dt + Sigma(t),dW(t) ] to zero. $A$ is a constant $dtimes d$ m...
Continuous Ocone Martingales as Weak Limits of Rescaled Martingales
ocone martingales rescaled martingales weak convergence
2009/4/29
Consider a martingale $M$ with bounded jumps and two sequences $a_n, b_n to infty$. We show that if the rescaled martingales
M^n_t =frac{1}{sqrt{a_n}}M_{b_n t}
converge weakly, then the limit is...
Optimal Control for Absolutely Continuous Stochastic Processes and the Mass Transportation Problem
Absolutely continuous stochastic process mass transportation problem Salisburyfi problem
2009/4/29
We study the optimal control problem for Rd-valued absolutely continuous stochastic processes with given marginal distributions at every time. When $d=1$, we show the existence and the uniqueness of a...
State Classification for a Class of Interacting Superprocesses with Location Dependent Branching
spatial structure interaction superprocess location dependent branching
2009/4/29
The spatial structure of a class of superprocesses which arise as limits in distribution of a class of interacting particle systems with location dependent branching is investigated. The criterion of ...
Quantitative Convergence Rates of Markov Chains: A Simple Account
Markov chain convergence rate mixing time drift condition minorisation condition total variation distance
2009/4/29
We state and prove a simple quantitative bound on the total variation distance after k iterations between two Markov chains with different initial distributions but identical transition probabilities....
We give another proof of the following result from a joint paper with Bálint Tóth: A Brownian motion reflected on an independent time-reversed Brownian motion is a Brownian motion.
Option Price When the Stock is a Semimartingale
Black-Scholes formula Meyer-Tanaka formula semimartingales
2009/4/29
The purpose of this note is to give a PDE satisfied by a call option when the price process is a semimartingale. The main result generalizes the PDE in the case when the stock price is a diffusion. It...
Some Extensions of an Inequality of Vapnik and Chervonenkis
Concentration of measure empirical processes
2009/4/29
The inequality of Vapnik and Chervonenkis controls the expectation of the function by its sample
average uniformly over a VC-major class of functions taking into account the size of the expectation...
Asymptotics for Products of Sums and U-statistics
central limit theorem lognormal distribution products of sums records U-statistics
2009/4/29
The product of subsequent partial sums of independent, identically distributed, square integrable, positive random variables is asymptotically lognormal. The result extends in a rather routine way to ...
Further Exponential Generalization of Pitman's 2M-X Theorem
Diffusion processes Generalization of Pitman's 2M-X Theorem
2009/4/29
We present a class of processes which enjoy an exponential analogue of Pitman's 2M-X theorem, improving hence some works of H. Matsumoto and M. Yor.