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Siyu Lv 《统计学通讯:理论与方法》2018,47(14):3360-3376
We first give the existence and uniqueness results for infinite horizon backward stochastic differential equations with Markov chains, taking advantage of the martingale representation theorem and fixed point principle. Then we prove the well-posedness results for infinite horizon reflected backward stochastic differential equations with Markov chains, by virtue of the Snell envelope theory and contraction mapping method. Comparison theorems for the above two kinds of equations are also obtained, via the linearization approach or properties of reflected backward stochastic differential equations, respectively. 相似文献
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K. Nyström 《随机性模型》2016,32(2):275-300
In this paper we study multidimensional reflected backward stochastic differential equations driven by Wiener-Poisson type processes. We prove existence and uniqueness of solutions, with reflection in the inward spatial normal direction, in the setting of certain time-dependent domains. 相似文献
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MAUD DELATTRE VALENTINE GENON‐CATALOT ADELINE SAMSON 《Scandinavian Journal of Statistics》2013,40(2):322-343
Abstract. We consider N independent stochastic processes (X i (t), t ∈ [0,T i ]), i=1,…, N, defined by a stochastic differential equation with drift term depending on a random variable φ i . The distribution of the random effect φ i depends on unknown parameters which are to be estimated from the continuous observation of the processes Xi. We give the expression of the exact likelihood. When the drift term depends linearly on the random effect φ i and φ i has Gaussian distribution, an explicit formula for the likelihood is obtained. We prove that the maximum likelihood estimator is consistent and asymptotically Gaussian, when T i =T for all i and N tends to infinity. We discuss the case of discrete observations. Estimators are computed on simulated data for several models and show good performances even when the length time interval of observations is not very large. 相似文献
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We consider some stochastic models that have been proposed for the trajectories of moving objects, including Brownian motion. This leads to the development of a general approach for dealing with paths including the use of functional stochastic differential equations. We then present an empirical example based on the surface drifting movements of a small satellite-linked radio transmitter tag after it detached from a whale shark in the western Indian Ocean. The daily estimates of the tag’s locations were determined from transmissions received at irregular times by polar-orbiting satellites of the Argos Data Collection and Location Service system. 相似文献
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Zhen Wu 《统计学通讯:理论与方法》2020,49(21):5356-5370
AbstractThis paper concerns a class of stochastic recursive zero-sum differential game problem with recursive utility related to a backward stochastic differential equation (BSDE) with double obstacles. A sufficient condition is provided to obtain the saddle-point strategy under some assumptions. In virtue of the corresponding relationship of doubly reflected BSDE and mixed game problem, a stochastic linear recursive mixed differential game problem is studied to apply our theoretical result, and here the explicit saddle-point strategy as well as the saddle-point stopping time for the mixed game problem are obtained. Besides, a numeral example is also given to demonstrate the result by virtue of partial differential equations (PDEs) computation method. 相似文献
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Since the seminal paper of Ghirardato (1997), it is known that Fubini theorem for non additive measures can be available only for functions as “slice-comonotonic” in the framework of product algebra. Later, inspired by Ghirardato (1997), Chateauneuf and Lefort (2008) obtained some Fubini theorems for non additive measures in the framework of product σ-algebra. In this article, we study Fubini theorem for non additive measures in the framework of g-expectation. We give some different assumptions that provide Fubini theorem in the framework of g-expectation. 相似文献
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UMBERTO PICCHINI REA DE GAETANO SUSANNE DITLEVSEN 《Scandinavian Journal of Statistics》2010,37(1):67-90
Abstract. Stochastic differential equations have been shown useful in describing random continuous time processes. Biomedical experiments often imply repeated measurements on a series of experimental units and differences between units can be represented by incorporating random effects into the model. When both system noise and random effects are considered, stochastic differential mixed-effects models ensue. This class of models enables the simultaneous representation of randomness in the dynamics of the phenomena being considered and variability between experimental units, thus providing a powerful modelling tool with immediate applications in biomedicine and pharmacokinetic/pharmacodynamic studies. In most cases the likelihood function is not available, and thus maximum likelihood estimation of the unknown parameters is not possible. Here we propose a computationally fast approximated maximum likelihood procedure for the estimation of the non-random parameters and the random effects. The method is evaluated on simulations from some famous diffusion processes and on real data sets. 相似文献
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In this paper, we introduce the concept of the p-mean almost periodicity for stochastic processes in non linear expectation spaces. The existence and uniqueness of square-mean almost periodic solutions to some non linear stochastic differential equations driven by G-Brownian motion are established under some assumptions for the coefficients. The asymptotic stability of the unique square-mean almost periodic solution in the square-mean sense is also discussed. 相似文献
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ABSTRACTIn this paper, we start with establishing the existence of a minimal (maximal) Lp (1 < p ? 2) solution to a one-dimensional backward stochastic differential equation (BSDE), where the generator g satisfies a p-order weak monotonicity condition together with a general growth condition in y and a linear growth condition in z. Then, we propose and prove a comparison theorem of Lp (1 < p ? 2) solutions to one-dimensional BSDEs with q-order (1 ? q < p) weak monotonicity and uniform continuity generators. As a consequence, an existence and uniqueness result of Lp (1 < p ? 2) solutions is also given for BSDEs whose generator g is q-order (1 ? q < p) weakly monotonic with a general growth in y and uniformly continuous in z. 相似文献
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Xi Chen 《统计学通讯:理论与方法》2013,42(14):2492-2514
As a continuous-time model, forward-backward stochastic differential equations (in short FBSDEs) have been successfully applied in mathematical finance, e.g., European option pricing for either a small or a large investor in a Markovian market. However, the correct FBSDEs model for a specific topic can neither be provided automatically by financial market nor derived from theory of mathematical finance. In this article, a nonparametric FBSDEs model is adopted for its flexibility and robustness, and the estimators of the functional coefficients of the FBSDEs model are obtained. The asymptotic properties of the estimators are also discussed. A simulation is performed to test the feasibility of our method. 相似文献
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Two Itô stochastic differential equation (SDE) systems are constructed for a Susceptible-Infected-Susceptible epidemic model with temporary vaccination. A constant number of new members enter the population and total size of the population is variable. Some conditions for disease extinction in the stochastic models are established and compared with conditions in deterministic one. It is shown that the two stochastic models are equivalent in the sense that their solutions come from same distribution. In addition, the SDE models are simulated and the equivalence of the two stochastic models is confirmed by numerical examples. The probability distribution for extinction is also obtained numerically, provided there exists a probability for disease persistence whereas the expected duration of epidemic is acquired when extinction occurs with probability 1. 相似文献
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Yasutaka Shimizu 《Scandinavian Journal of Statistics》2017,44(4):951-988
Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent but numerically unstable in the sense of large standard deviations under finite samples when the noise process has jumps. We propose a filter to cut large shocks from data and construct the same LSE from data selected by the filter. The proposed estimator can be asymptotically equivalent to the usual LSE, whose asymptotic distribution strongly depends on the noise process. However, in numerical study, it looked asymptotically normal in an example where filter was chosen suitably, and the noise was a Lévy process. We will try to justify this phenomenon mathematically, under certain restricted assumptions. 相似文献
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《Scandinavian Journal of Statistics》2018,45(1):62-86
The concept of causality is naturally related to processes developing over time. Central ideas of causal inference like time‐dependent confounding (feedback) and mediation should be viewed as dynamic concepts. We shall study these concepts in the context of simple dynamic systems. Time‐dependent confounding and its implications are illustrated in a Markov model. We emphasize the distinction between average treatment effect, ATE, and treatment effect of the treated, ATT. These effects could be quite different, and we discuss the relationship between them. Mediation is studied in a stochastic differential equation model. A type of natural direct and indirect effects is considered for this model. Mediation analysis of discrete measurements from such processes may give misleading results, and one needs to consider the underlying continuous process. The dynamic and time‐continuous view of causality and mediation is an essential feature, and more attention should be payed to the time aspect in causal inference. 相似文献
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MARTIN BACHMAIER 《Scandinavian Journal of Statistics》2011,38(1):147-168
Abstract. A test for two‐sided equivalence of means has been developed under the assumption of normally distributed populations with heterogeneous variances. Its rejection region is limited by functions ± h that depend on the empirical variances. h is stated implicitly by a partial differential equation, an exact solution of which would provide a test that is exactly similar at the boundary of the null hypothesis of non‐equivalence. h is approximated by Taylor series up to third powers in the reciprocal number of degrees of freedom. This suffices to obtain error probabilities of the first kind that are very close to a nominal level of α = 0 . 05 at the boundary of the null hypothesis. For more than 10 data points in each group, they range between 0.04995 and 0.05005, and are thus much more precise than those obtained by other authors. 相似文献
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Accelerating inference for diffusions observed with measurement error and large sample sizes using approximate Bayesian computation 总被引:1,自引:0,他引:1
《Journal of Statistical Computation and Simulation》2012,82(1):195-213
In recent years, dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However, it is often computationally unfeasible to apply exact statistical methodologies in the context of large data sets and complex models. This paper considers a nonlinear stochastic differential equation model observed with correlated measurement errors and an application to protein folding modelling. An approximate Bayesian computation (ABC)-MCMC algorithm is suggested to allow inference for model parameters within reasonable time constraints. The ABC algorithm uses simulations of ‘subsamples’ from the assumed data-generating model as well as a so-called ‘early-rejection’ strategy to speed up computations in the ABC-MCMC sampler. Using a considerate amount of subsamples does not seem to degrade the quality of the inferential results for the considered applications. A simulation study is conducted to compare our strategy with exact Bayesian inference, the latter resulting two orders of magnitude slower than ABC-MCMC for the considered set-up. Finally, the ABC algorithm is applied to a large size protein data. The suggested methodology is fairly general and not limited to the exemplified model and data. 相似文献
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随机波动HJM框架下信用利差模型及实证研究 总被引:1,自引:0,他引:1
将随机波动引入到具有违约风险的HJM模型中,基于无套利条件推导得出随机波动HJM模型框架下信用利差的漂移项限制条件,从而构建了随机波动HJM框架下的信用利差模型,并基于波动率结构的适当设定对模型进行马尔科夫简化,进而利用该模型对中国可违约债券市场信用利差的动态特性进行实证分析。结果发现:短期信用利差的动态特性具有显著的随机波动特征,而随机波动HJM框架下的信用利差模型可以很好地刻画中国可违约债券市场信用利差的动态特性。 相似文献
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We propose a wavelet based stochastic regression function estimator for the estimation of the regression function for a sequence of mixing stochastic process with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator are investigated. It is found that the estimators have similar properties to their counterparts studied earlier in literature. 相似文献
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Muhammad Hanif 《统计学通讯:理论与方法》2013,42(9):1896-1910
In this paper, we study the non parametric estimation of drift coefficient and diffusion coefficient in the second-order diffusion equation by using the asymmetric kernel functions, based on the difference of discrete time observations. The basic idea relies upon replacing the symmetric kernel by asymmetric kernel and provides a new way of obtaining the non parametric estimation for second-order diffusion equation. Under the appropriate assumptions, we prove that the proposed estimators of second-order diffusion equation are consistent and asymptotically follow normal distribution. 相似文献