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What do card shuffling, volume growth, and Harnack inequalities have to do with each other? They all arise in the study of random walks on groups. Probability on groups is concerned with probabil...
Let Ω ⊂ Rn be a bounded domain and for x ∈ Ω let τ(x) be the expected exit time from Ω of a diffusing particle starting at x and advected by an incompressible flow u. We are in...
This paper is concerned with the analysis of the average error in approximating the global minimum of a 1-dimensional, time-homogeneous diffusion by non-adaptive methods. We derive the limiting distri...
In this paper we consider the problem of calculating the quantiles of a risky position,the dynamic of which is described as a continuous time regime-switching jump-diffusion, by using Fourier Transfor...
We provide a complete characterization of the class of one-dimensional time-homogeneous di usions consistent with a given law at an exponentially distributed time using classical results in di usion t...
We consider a multidimensional diffusion X with drift coefficient b({\alpha},X(t)) and diffusion coefficient {\epsilon}{\sigma}({\beta},X(t)). The diffusion is discretely observed at times t_k=k{\Delt...
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...
We discuss suitable classes of diffusion processes, for which functionals relevant to finance can be computed via Monte Carlo methods. In particular, we construct exact simulation schemes for processe...
We analyze in this paper the asymptotic behavior of the specification test of Aït-Sahalia (1996) for the stationary density of a diffusion process, but when the diffusion is not stationary. We co...
Abstract: We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these probl...
Abstract: We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obta...
Abstract: The uniqueness argument in the proof of Theorem 5, p. 483, of "Small noise asymptotics for invariant densities for a class of diffusions: a control theoretic view, J. Math. Anal. and Appl. (...
Abstract: We address the question of the trends to equilibrium for a large class C of relativistic diffusions. We show the existence of a spectral gap using the Lyapounov method and deduce the exponen...
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting dist...

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