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The Wronskian parameterizes the class of diffusions with a given distribution at a random time
class of diffusions distribution random time Probability
2012/6/3
We provide a complete characterization of the class of one-dimensional time-homogeneous diffusions consistent with a given law at an exponentially distributed time using classical results in diffusion...
Tunneling and Metastability of continuous time Markov chains II, the nonreversible case
Metastability Tunneling Markov processes
2012/5/2
We proposed in \cite{bl2} a new approach to prove the metastable behavior of reversible dynamics based on potential theory and local ergodicity. In this article we extend this theory to nonreversible ...
Slow Manifolds for Multi-Time-Scale Stochastic Evolutionary Systems
Slow Manifolds Multi-Time-Scale Stochastic Evolutionary Systems Probability
2012/5/2
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic ...
On the time inhomogeneous skew Brownian motion
Skew Brownian motion Local times Stochastic differential equation balayage formula Skorokhod problem
2012/4/3
This paper is devoted to the construction of a solution for the "Inhomogenous skew Brownian motion" equation, which first appeared in a seminal paper by Sophie Weinryb, and recently, studied by \'{E}t...
Interfacial Phenomena and Natural Local Time
Advection-dispersion discontinuous diffusion skew Brownian motion mathematical local time natural local time
2012/4/1
This article addresses a modification of local time for stochastic processes, to be referred to as `natural local time'. It is prompted by theoretical developments arising in mathematical treatments o...
Stability of nonlinear stochastic Volterra difference equations with continuous time
Nonlinear stochastic difference equations Stability Lyapunov functional construction Continuous time
2011/11/4
In recent years, many authors investigated the systems of stochastic difference equations with discrete time or the systems of numerical solution for stochastic difference equations with continue time...
Uniform moment bounds of multi-dimensional functions of discrete-time stochastic processes
stochastic stability Markov chains uniform moment bounds invariant distributions stochastic control
2011/7/24
Abstract: We establish conditions for uniform $r$-th moment bound of certain $\R^d$-valued functions of a discrete-time stochastic process taking values in a general metric space. The conditions inclu...
Asymptotic behaviour of first passage time distributions for Levy processes
Levy processes first passage time distribution local limit theorems fluctuation theory
2011/7/22
Abstract: Let $X$ be a real valued L\'evy process that is in the domain of attraction of a stable law without centering with norming function $c.$ As an analogue of the random walk results in \cite{vw...
Abstract: In this paper, we want to investigate some kind of Dynkin's game under ambiguity which is represented by Backward Stochastic Differential Equation (shortly BSDE) with standard generator func...
Commuting time geometry of ergodic Markov chains
Commuting time geometry ergodic Markov chains Probability
2011/7/13
Abstract: We show how to map the states of an ergodic Markov chain to Euclidean space so that the squared distance between states is the expected commuting time. We find a minimax characterization of ...
On the existence of a time inhomogeneous skew Brownian motion and some related laws
time inhomogeneous skew Brownian motion Probability
2011/7/12
Abstract: This article is devoted to the construction of a solution for the "skew inhomogeneous Brownian motion" equation, which first appear in a seminal paper by Sophie Weinryb (1983). We investigat...
Joint Extremal Behavior of Hidden and Observable Time Series
tail chain time series joint extremal behavior ARCH
2011/7/3
Abstract: We analyze the joint extremal behavior of two real-valued processes (X_t) and (Y_t) which can be interpreted as an observable and an unobservable time series. Our analysis is motivated by th...
Pointwise stabilization of discrete-time matrix-valued stationary Markov chains
Markovian jump linear system pointwise stabilization random products of matrices
2011/7/1
Abstract: Let $(\Omega,\mathscr{F},\mathbb{P})$ be a probability space and $\bS=\{\mathrm{S}_1,...,\mathrm{S}_K\}$ a discrete-topological space that consists of $K$ real $d$-by-$d$ matrices, where $K$...
Numerical methods for the exit time of a piecewise-deterministic Markov process
exit time piecewise deterministic Markov processes quantization
2010/12/31
We present a numerical method to compute the survival function and the moments of the exit time for a piecewise-deterministic Markov process (PDMP).
Filtering of continuous-time Markov chains with noise-free observation and applications
Filtering of continuous-time Markov chains noise-free observation applications
2010/9/1
Let X be a continuous-time Markov chain in a finite set I, let h be a mapping of I onto another set, and let Y be defined by Yt = h(Xt), (t ≥ 0). We address the filtering problem
for X in terms of th...