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George S Sacerdote 《Advances in Mathematics》1975,17(3):261-280
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Giraudo Maria Teresa Sacerdote Laura Zucca Cristina 《Methodology and Computing in Applied Probability》2001,3(2):215-231
A reliable Monte Carlo method for the evaluation of first passage times of diffusion processes through boundaries is proposed. A nested algorithm that simulates the first passage time of a suitable tied-down process is introduced to account for undetected crossings that may occur inside each discretization interval of the stochastic differential equation associated to the diffusion. A detailed analysis of the performances of the algorithm is then carried on both via analytical proofs and by means of some numerical examples. The advantages of the new method with respect to a previously proposed numerical-simulative method for the evaluation of first passage times are discussed. Analytical results on the distribution of tied-down diffusion processes are proved in order to provide a theoretical justification of the Monte Carlo method. 相似文献
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We consider a sample of i.i.d. times and we interpret each item as the first-passage time (FPT) of a diffusion process through a constant boundary.
The problem is to estimate the parameters characterizing the underlying diffusion process through the experimentally observable
FPT’s. Recently in Ditlevsen and Lánsky (Phys Rev E 71, 2005) and Ditlevsen and Lánsky (Phys Rev E 73, 2006) closed form estimators
have been proposed for neurobiological applications. Here we study the asymptotic properties (consistency and asymptotic normality)
of the class of moment type estimators for parameters of diffusion processes like those in Ditlevsen and Lánsky (Phys Rev
E 71, 2005) and Ditlevsen and Lánsky (Phys Rev E 73, 2006). Furthermore, to make our results useful for application instances
we establish upper bounds for the rate of convergence of the empirical distribution of each estimator to the normal density.
Applications are also considered by means of simulated experiments in a neurobiological context.
相似文献
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David Gilat Isaac Meilijson Laura Sacerdote 《Stochastic Processes and their Applications》2018,128(6):1849-1856
For a martingale starting at with final variance , and an interval , let be the normalized length of the interval and let be the normalized distance from the initial point to the lower endpoint of the interval. The expected number of upcrossings of by is at most if and at most otherwise. Both bounds are sharp, attained by Standard Brownian Motion stopped at appropriate stopping times. Both bounds also attain the Doob upper bound on the expected number of upcrossings of for submartingales with the corresponding final distribution. Each of these two bounds is at most , with equality in the first bound for . The upper bound on the length covered by during upcrossings of an interval restricts the possible variability of a martingale in terms of its final variance. This is in the same spirit as the Dubins & Schwarz sharp upper bound on the expected maximum of above , the Dubins & Schwarz sharp upper bound on the expected maximal distance of from , and the Dubins, Gilat & Meilijson sharp upper bound on the expected diameter of . 相似文献
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Gilat David Meilijson Isaac Sacerdote Laura 《Journal of Theoretical Probability》2022,35(3):1952-1955
Journal of Theoretical Probability - For an $${\text {L}}_2$$ -bounded martingale starting at 0 and having final variance $$\sigma ^2$$ , the expected local time at $$a \in \text {R}$$ is at most... 相似文献
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Enrico Bibbona Laura Sacerdote Emiliano Torre 《Methodology and Computing in Applied Probability》2016,18(3):765-783
This paper investigates the probabilistic properties that determine the existence of space-time transformations between diffusion processes. We prove that two diffusions are related by a monotone space-time transformation if and only if they share the same serial dependence. The serial dependence of a diffusion process is studied by means of its copula density and the effect of monotone and non-monotone space-time transformations on the copula density is discussed. This approach provides a methodology to build diffusion models by freely combining prescribed marginal behaviors and temporal dependence structures. Explicit expressions of copula densities are provided for tractable models. 相似文献
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Conditions on the boundary and parameters that produce ordering in the first passage time distributions of two different diffusion processes are proved making use of comparison theorems for stochastic differential equations. Three applications of interest in stochastic modeling are presented: a sensitivity analysis for diffusion models characterized by means of first passage times, the comparison of different diffusion models where first passage times represent an important feature and the determination of upper and lower bounds for first passage time distributions. 相似文献
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