بررسی مدل‌های دیفرانسیل تصادفی بر اساس دیدگاه آماری و کاربردهای آن

نویسندگان
1 دانشگاه کاشان
2 دانشگاه پیام نور
چکیده
در این مقاله از دیدگاه استنباط آماری، مدل‌های معادلات دیفرانسیل تصادفی مورد مطالعه قرار می‌گیرند. یک حالت ناهمگن از یک فرایند انتشار با ضریب کاهش سرعت وابسته به زمان و مدل‌های معادلات دیفرانسیل تصادفی با اثرات تصادفی بررسی می‌شود و یک تقریب برای معادله دیفرانسیل تصادفی غیر‌خطی ارائه می‌شود. همچنین به کمک تحلیل‌های سری زمانی و روش‌های آماری، پارامترهای مدل‌های معادلات دیفرانسیل تصادفی براورد می‌شوند. در پایان کاربرد مفصل ناوردا در مدل‌بندی معادلات دیفرانسیل تصادفی بیان می‌شود. در هر از این حالت‌ها تابع چگالی احتمال فرایند و توابع روند محاسبه می‌شوند و استنباط‌های آماری نظیر براورد نقطه‌ای، براورد فاصله‌ای، انتخاب بهترین مدل و تحلیل‌های عددی و شبیه‌سازی در معادلات دیفرانسیل تصادفی انجام می‌شوند.
کلیدواژه‌ها

عنوان مقاله English

Investigating stochastic differential models based on the statistical point of view and its applications

نویسندگان English

Mehdi Shams 1
Gholamreza Hesamian 2
1 University of Kashan
2 Payame Noor University
چکیده English

In this paper, the probability density function of the process, its trend functions, the maximum likelihood estimate and the confidence interval of the parameters are calculated. This paper investigates a nonhomogeneous state of a diffusion process with a time-dependent velocity reduction coefficient. First, the process probability density function and trend functions are calculated and then, using discrete sampling, statistical inferences such as estimating the parameters by the maximum likelihood method, finding the distribution of the obtained estimators and the confidence interval of the parameters are performed. Finally, for the simulated data, the applications of this model are introduced.



In this paper, from the point of view of statistical inference, stochastic differential equation models are studied. A heterogeneous case of a diffusion process with time-dependent deceleration coefficient and stochastic differential equation models with random effects are investigated and an approximation for the nonlinear stochastic differential equation is presented. Also, with the help of time series analysis and statistical methods, the parameters of stochastic differential equation models are estimated.At the end, the application of invariant copulas in the modeling of stochastic differential equations is expressed. In each of these cases, the process probability density function and trend functions are calculated, and statistical inferences such as point estimation, interval estimation, selection of the best model, and numerical analyzes and simulations are performed in stochastic differential equations.


کلیدواژه‌ها English

Wiener process
Stochastic Differential Equations
Maximum Likelihood estimation
Akaike information criterion
Parameter estimation
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