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Hitting probabilities for systems of non-linear stochastic heat equations with additive noise
Hitting probabilities systems of non-linear stochastic heat equations space-time white noise capacity Hausdor measure
2009/6/12
We consider a system of d coupled non-linear stochastic heat equations in spatial dimension 1 driven by d-dimensional additive space-time whitenoise. We establish upper and lower bounds on hitting pro...
Transformations of infinitely divisible distributions via improper stochastic integrals
improper stochastic integral independently scattered random measure innitely divisible distribution Levy measure
2009/6/12
Transformations of infinitely divisible distributions via improper stochastic integrals.
Spatial birth and death processes as solutions of stochastic equations
spatial birth death processes stochastic equations
2009/6/12
Spatial birth and death processes as solutions of stochastic equations .
Two families of improper stochastic integrals with respect to Lévy processes
stochastic integrals Lévy processes two families
2009/6/12
Two families of improper stochastic integrals with respect to Lévy processes.
On some recent aspects of stochastic control and their applications
Controlled diffusions dynamic programming maximum principle viscosity solutions
2009/5/18
This paper is a survey on some recent aspects and developments in stochastic control. We discuss the two main historical approaches, Bellman's optimality principle and Pontryagin's maximum principle, ...
Nonclassical stochastic flows and continuous products
stochastic flows continuous products noise stability sensitivity
2009/5/18
Contrary to the classical wisdom, processes with independent values (defined properly) are much more diverse than white noises combined with Poisson point processes, and product systems are much more ...
Large deviations and stochastic calculus for large random matrices
large deviations random matrices non-commutative measure integration.
2009/5/18
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory e...
Stochastic differential equations with jumps
stochastic differential equations jumps martingale problems pathwise uniqueness Harnack inequality
2009/5/18
This paper is a survey of uniqueness results for stochastic differential equations with jumps and regularity results for the corresponding harmonic functions.
An essay on the general theory of stochastic processes
General theory of stochastic processes Enlargements of filtrations Random times Submartingales Stopping times Honest times Pseudo-stopping times
2009/5/18
This text is a survey on the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which where d...
Stochastic analysis of Bernoulli processes
Malliavin calculus Bernoulli processes discrete time chaotic calculus functional inequalities option hedging
2009/5/18
These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include ...
Mild Solutions of Quantum Stochastic Differential Equations
Quantum stochastic differential equation stochastic differential equation mild solution
2009/5/4
We introduce the concept of a mild solution for the right Hudson-Parthasarathy quantum stochastic differential equation, prove existence and uniqueness results, and show the correspondence between our...
L1-Norm of Infinitely Divisible Random Vectors and Certain Stochastic Integrals
Infinitely divisible random variables stochastic integrals
2009/5/4
Equivalent upper and lower bounds for the L1 norm of Hilbert space valued infinitely divisible random variables are obtained and used to find bounds for different types of stochastic integrals.
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...
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...
A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand
heat equation white noise stochastic partial differential equations
2009/4/29
We give a new representation of fractional Brownian motion with Hurst parameter $Hleqfrac{1}{2}$ using stochastic partial differential equations. This representation allows us to use the Markov proper...